Which is the best course to pursue after the completion of Master of Science in chemistry?

For a higher qualifications, you can pursue Ph.D and become a professor.

If you have completed your Master's degree, then you can apply for many government jobs or private jobs like - SSC CGL, etc. But, if you want to continue your studies, then you can do Ph.D. from IISC or IIT's. To do integrated Ph.D. courses at IISC, you have to prepare for its entrance exam - IIT J