Last year I had H1B Petition with employer 'A' that was valid for 1 year, I traveled to the US for 2 months on that visa. After that, it expired. Now my employer is not ready to file cap exempt visa. What are the options for me to pursue my US career opportunity? Can I simply switch my job and my new employer can file cap exempt or I need some approval from my old employer.
Just moving brhans' comment to an answer:
You are not tied to your old employer. A new employer can file a new cap-exempt "transfer" of your H-1B for you and you can move jobs as soon as they've submitted the correct paperwork.