I had the same problem with QIC, after the 1st year they only offered TPL(3rd party) so I switched to Doha Insurance Company in Najma.They never asked for any clearance from QIC,just the copy of the previous insurance of my car.Until now my insurance is Doha Insurance but I got 3rd party only since I had no claim or never got into accident last year.

You can transfer to other insurance company but the problem with some insurance company is you have to pay a certain amount even if you got the full insurance.