You can extend your residence permit for employment purposes by a request on enterhungary.gov.hu or in person at the Immigration Office. For the extension of your permit, please make sure the followings:
have AIESEC notified about the extension (by you and your employer as well)
a valid Student Certificate was provided and accepted by AIESEC (more about SC here)
you have not passed the extension request deadline of 45 days before your current permit expires
About the details of the permit and the policies of the extension, you can read more on this website.