Yes. There are some instances when you may be required to pay a new mortgage loan insurance premium when switching lenders, such as:
When your loan amount increases
When you extend the amortization period
That said, you should inform your new lender if you have mortgage loan insurance on your existing loan to avoid paying the premiums twice. Simply ask for the certificate number from your current lender. Consider asking for a copy of the insurance certificate when getting your mortgage contract.
You will be required to sign the registration documents obtained with your mortgage contract, usually with the assistance of your lawyer or notary.