H1B Transfer and Extension possibilities

Hi Friends,
I’m based out of India and my Current H1b visa with my employer had expired in June 2020 . I am planning to join another employer for better career. Is it possible for my my new employer to transfer my visa and initiate new extension for me? If yes, please suggest with the list of steps possible for my employer to move on with my visa. You valuable inputs on this would be highly appreciated.

Thank You