Can You Leave Work Early without Permission?
Question

I am in charge of a government organization, and sometimes I leave my office on personal errands. I do not have a direct superior whom I could ask for permission to leave. My leaving is during work hours but it does not have any impact on the organization. With the mobile phone, it is possible for people to contact me at any time for work purposes, if need be. Usually I stay longer in my office when work is finished. What is the Islamic ruling on the time that I spend outside my office? Please advise us, may Allah bless you.
Praise be to Allah.The employee must be present and remain in the workplace for the duration of the working hours agreed upon, whether he has work or not , because the job or the contract requires that. The employee is a hired worker whose benefit is measured by the time he spends on the job. Therefore, he must set aside this time for work only. 
Moreover, if the matter were left to the worker’s discretion, and he were told that he should only come when there is work, companies would fail and work would not be done, because it would not be possible to manage the situation.
This is the basic principle regarding employment; they come under the heading of contracts of hire that are based on time worked.
But an exception is made from that if the employee needs to leave for some errand or purpose that it is difficult to delay until after working hours, in which case he may leave with the permission of the management .
If the situation is as you described, that you are in charge of this organization and there is no one whom you may ask for permission to leave, then we say: it is permissible for you to go out for an urgent need that it is difficult to delay until after working hours, but you should regard yourself as being any other employee, and you should not allow yourself more than you would allow them. Rather you should be an example to others, and you should be more strict with yourself than you would with them. What happens in reality if the employees see their boss leaving is that they will take the matter of leaving lightly and they will slow down in their work, and this will lead to much mischief.
Having a mobile phone is not sufficient, and neither is your staying after working hours, because your duty must be done during working hours, not afterwards. This comes under the heading of trusts with which a person is entrusted, whether the boss who will hold him accountable is present or not . Allah, may He be exalted, says (interpretation of the meaning):
{Indeed, Allah commands you to render trusts to whom they are due.} [an-Nisa’ 4:58]
Ibn Kathir (may Allah have mercy on him) said in his Tafsir (1/673): 
“Here Allah, may He be exalted, tells us that He enjoins us to render trusts to those to whom they are due. In the hadith of al-Hasan, from Samurah, it says that the Messenger of Allah (blessings and peace of Allah be upon him) said: “Render the trust to the one who entrusted you with it, and do not betray the one who betrays you.” Narrated by Ahmad and the compilers of the Sunans. This includes all trusts that are enjoined upon a person, including the rights that Allah, may He be glorified and exalted, has over His slaves, such as prayer, zakah, expiation, vows, fasts and so on, with which he is entrusted and no people can see, as well as the rights that people have over one another, such as items left for safekeeping and other things with which they entrust one another, without anyone being aware of it. Allah, may He be glorified and exalted, has commanded us to fulfill them, so the one who does not do that in this world will be held accountable for it on the Day of Resurrection.”
Work is only neglected or not done because of careless attitudes on the part of managers and bosses who leave the workplace whenever they wish. In contrast to that, you see that in organizations where managers come early and rarely leave, the workers are disciplined and do their work properly.
The manager should understand that part of the work for which he is responsible is supervising employees, following up on them, evaluating their work, advising and directing them, and making them aware that he is watching them and will call them to account.
Because of the importance of this topic and the fact that there are many questions about it, we will quote here a number of fatwas from scholars concerning it:

The scholars of the Permanent Committee for Ifta’ were asked: Employees who are required to work set hours leave during these hours to engage in buying and selling without permission. What is the ruling on this behaviour of theirs?

They replied: 
“It is not permissible for the employee to leave during working hours to buy and sell, whether he has permission from his boss or not, because this is contrary to the instructions of those in authority, who do not allow that. Moreover, this will lead to the work with which he has been entrusted not being done, as a result of which the Muslims who come to deal with paperwork will be unable to get the service they need, and the employee will fail to do that work properly. Abu Ya‘la and al-‘Askari narrated from ‘A’ishah in a marfu‘ report that the Prophet (blessings and peace of Allah be upon him) said: “Allah loves, if one of you performs a task, that he should do it well.” Al-Bayhaqi and at-Tabarani narrated a similar report. " (Fatawa al-Lajnah ad-Da’imah 23/415).

Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) was asked: During official working hours, there are some people who come half an hour late, or they leave half an hour before the end of working hours, and sometimes they are an hour or more late. What is the ruling on that?

He replied: 
“It is obvious that this does not require an answer, because compensation must be for something in return. Just as the employee would not like the state to deduct anything from his salary, he should not deduct anything from the rights of the state. So it is not permissible for a person to come late during working hours, or to leave early.
Questioner: But some people argue that there was no work in the first place, because there is little work.
Shaykh: What matters is that you are assigned to spend a certain amount of time, not do specific work. In other words, you have been told: this salary is in return for being present from this time to that time, whether there is work or not. So long as the salary is connected to time, then you must be present during this time, otherwise our earnings for the hours we did not attend are haram earnings." (Liqa’ al-Bab al-Maftuh  9/14).

He (may Allah have mercy on him) was also asked: Some employees leave before the end of working hours, or during working hours, or they come late. What is the ruling on that?

He replied: 
“It is not permissible for the employee to leave before the end of working hours, or to come late, or to leave during working hours, because these working hours belong to the state, in return for which the employee receives a salary from the public treasury. But what usually happens is that if there is a need for him to leave during working hours, and he asks permission from his boss or manager, and the work is not impacted by his leaving, then I hope that there is nothing wrong with that.”

Shaykh Salih al-Fawzan (may Allah preserve him) was asked: Some employees who have little work to do leave at midday, before the end of working hours, to eat lunch with their wives, then they come back and remain in their offices until the end of working hours. Is doing that permissible, and what advice would you give them?

He replied:
“The employee is required to be present in the workplace from the beginning of working hours until the end, and it is not permissible for him to go out to his house or to take care of his private affairs during working hours. Rather he must remain in the workplace, even if the work is slow, because the working hours belong to work and not to him, because this time has been bought from him in return for the salary that he receives. Therefore it is not permissible for him to deduct any time for his personal affairs except with an excuse that is approved of according to the rules of his workplace.”

Shaykh Ibn Jibrin (may Allah preserve him) was asked: Is it permissible for a worker to leave during working hours on a regular basis, on the grounds that there is no work for him to do, even though his salary is large in relation to the small amount of work that he does?

He replied: 
“The employee should not leave his workplace until the working hours end, even if he has nothing to do, regardless of whether his salary is great or small. But if something comes up and something happens to him that compels him to leave, such as sickness or some urgent matter for which he has no option but to leave, then he may do that, and he should come back after dealing with that matter. That is because his time belongs to the state or the company for which he works, unless his work is a specific task, in which case he may finish that specific task then leave and go wherever he wants. And Allah knows best." (Fatawa Muhimmah li Muwazzaf al-Ummah)
For more, please see this category: Ruling on Jobs
And Allah knows best.