Aerospace engineers design, develop, and test aircraft, spacecraft, rockets and missiles, and supervise the production of these products.They also may specialize in a particular type of aerospace product, such as commercial aircraft, military fighter jets, helicopters, spacecraft, or missiles and rockets, and may become experts in aerodynamics, thermodynamics, celestial mechanics, propulsion, acoustics, or guidance and control systems. So I would suggest you to give Gate exam to get admission in M.Tech in Aerospace. Also, once you clear it you can either go for higher studies or you can also try for PSU recruitment as these will be the first step to build your career in this branch but yes, what all IITs and PSUs will be accepting Aerospace specialisation will vary accordingly which you need to check individually.

Hope this helps!!!