When you have such a large opening around the liner a large amount of the hot air generated from the wood stove will be rising up into the chimney cavity.
Chimney liner block off plate.
The block off plate can be made from most any non combustible material.
Without one the flue liner which should be insulated and the stove will try to heat the mass of masonry that is exposed to the outdoors.
It is very common to have to ovalize a short section of the liner in order to pass the liner through the throat damper.
This can result in a significant cooling of the stove and large heat loss.
This will prevent any airflow through the area around the liner.
To prevent this from happening install a block off plate.
Some are better than others.
This opening will vary in size but generally you will be installing a 6 or 8 chimney liner.
The damper sealing kit is designed to seal off your damper around your stainless steel chimney liner kit when installing a fireplace insert or a freestanding stove.
The block off plate is a fail for now we could not get the liner off the flue collar at the insert level in order to get the insert free we would have had to setup a ladder and climb the chimney about 35ft off the ground grade is 10ft below fireplace chimney is about 25ft and disconnect the liner at the top and lift it off i personally.
Heavy aluminum 26 or 24 ga sheet metal both work.
Top plates and caps can be ordered through most liner companies.
If you have an internal chimney then insulation is better but you could get away with a good block off plate and stuffing some mineral wool down a couple of feet from the top.