Question: I am part of a software development team in a big corporation. The team consists of the manager, several developers and one senior developer. The senior developer position recently became vacant and eveyone wants it, of course.

So I am applying for this position, and so does everyone else in the team. However, I believe that my chances to get that position are quite high. In fact, I have reason to believe that some of those people who make the decision about who gets the position have already decided to favor me.

Currently there is a very good relationship within the team, but the direct competition situation we are now getting placed in is already showing some signs of strain on it. I am worried that when I get the position, the other teammembers will become jealous of me and our relationship could become much worse.

Should I get the position, what can I do to prevent jealousy from the other team members from destroying my relationship with them?

Answer: 
There are two possible, mutually exclusive outcomes:

1. The aggressiveness dies down as management announces the winner, and everyone reconciles with the outcome and goes back to the grind.
2. The rancor persists.

All you can do is make it clear to everyone that you'll work with the winner, whoever they are, way before the management hands the decision. Keep up the team-oriented working style so that if the winner is you, the team members can see for themselves that the management decision to declare you the winner makes sense, even if they may not like the decision. If the team members believe that you are the least qualified to be the senior developer, the rancor may persist for some time.In which case, you'll have to look for ways to grow into the job and grow into the job. Fast.

I am not sure that getting the staff to like the management decision to declare you the winner should be the goal. Getting them to live with the decision is probably easier to achieve and the more realistic goal.
Jealousy is going to happen and that is not the problem to manage. 
If they did not think they deserved the position they would not have applied. 

Are they going to respect you as lead developer and work effectively is what you need to manage. If you are not respected in your current role then you will not be respected as lead. As lead facilitate and communicate over making design decisions yourself.

Don't act like you expect to get the position. That will not help harmony.