If my insurance refuses to pay the 3rd party. Am I still liable to compensate the 3rd party?

[>take]

I was in an accident and was at fault, there was a 3rd party involved. I have a Question - if my insurance refuses to pay the 3rd party am I still liable to compensate the 3rd party?

Your question is not clear - why your insurance company is not liable to pay?
They have to pay for all the liabilities if they are not excluded.