How should I handle a change of address for a Student Pilot License in the USA? I have moved to another place from current address with in same city, Do I have to change my address to the new one on my FAA Student Pilot License? If yes, how do I do it?
You can change your address with the FAA online.  You do not need to get a new plastic certificate.

http://www.faa.gov/licenses_certificates/airmen_certification/airmen_services/