You can do a masters and again a PhD if you want to study further. Else, you can go for a job after B.Tech as a fresher.
When I researched on the subject I found that there are many colleges in India which offer masters in aerospace engineering, for example, leading IITs, IISC Bangaluru, Institute of Aeronautical Engineering Andhra Pradesh, DIAT Pune, IIST Kerala, IIAEM Bangaluru, Jain University Bangaluru, IIIT Bangaluru, UPES Dehradun etc.
PhD in aerospace engineering is provided by institutes like IISC Bangaluru, UPES Dehradun, Indian Institute of space science and technology Thiruvananthapuram, many leading IITs etc.
Apart from that, if you are interested in a job you can go for that too. Aerospace engineers may work in the field of aviation, spacecrafts or defense systems. Aviation is a huge industry nationally and worldwide. So I believe you can get good jobs in this field if you venture thoroughly. The jobs may be in the area of flight security, maintenance, design and development in the field of navigation and control etc., in-flight entertainment (IFE) development, spacecraft design, testing etc.
USA, France, Germany, Canada and UK are the countries having the most advanced aerospace infrastructure. You may foresee yourself working in these countries at the apex of your career.