Assigning an existing life policy to a bank instead of taking a new mortgage life policy

I wasn't sure if this would be better in the insurance section or here.

Separate to my current mortgage life insurance policy I also have a term assurance plan.
I will soon be taking out a second mortgage.
Is it possible to assign an interest in my term assurance policy to the bank instead of taking out a third life policy?
The remaining term on the existing term plan is longer than the new mortgage term and the sum assured is five times the loan amount.
Thanks.