I have recently purchased a home with a wood burner add on to the regular forced air heat pump my question is do I need to keep the blower constantly running on the back of the wood burner to circulate the warm or let the blower on my heat pump run to circulate the warm air from the wood burner thanks for your help

There will not be an exact answer to this as it will depend on the layout of your house, how close registers and cold air return is to the wood burner, etc.

I would try it each way for a week - and decide from there which way the house is more comfortable.