when you say" visit visa", do you mean Business visit visa? If so, you have 2 options:
1. to enter qatar under your business visa and to exit it. Then your new company can apply for your work visa
2. to enter qatar under your business visa and to obtain a NOC letter from your current sponsor. In this case you don't need to exit qatar. Your new company can apply for your work visa, and you can start working with them basically immediately, since you are already in qatar. so if your current sponsor is willing to give you a NOC, this is definitely a better option.
when you say" visit visa", do you mean Business visit visa? If so, you have 2 options:
1. to enter qatar under your business visa and to exit it. Then your new company can apply for your work visa
2. to enter qatar under your business visa and to obtain a NOC letter from your current sponsor. In this case you don't need to exit qatar. Your new company can apply for your work visa, and you can start working with them basically immediately, since you are already in qatar. so if your current sponsor is willing to give you a NOC, this is definitely a better option.