NO NEED TO EXIT.

Since the old sponsor is ready to give NOC, you may get a letter on his company letter head saying taht he has no problem to transfer your visa to the nw company. There is an Arabic format of letter.

PRO of your new company will tell you , what you should exactly do. I knwo one person like this, who is workign now in the new company for the last one month. His visa processing is going on.