Yes, you can do the same and if you want to go for M.Tech through Gate so you can write the Gate exam in any specific branch but the eligibility criteria and the list of courses offered vary college to college. Some of the IITs which offer M.Tech in Aerospace Engineering are mentioned below -

IIT Bombay
IIT Kharagpur
IIT Madras
IIT Kanpur
IIST , Thiruvanatapuram

Hope this helps!!!