Chimney Damp - Gas Fire

First time poster.

Tldr: bedroom wall around chimney location has damp. Gas fire downstairs now back in commission and new cowel on top of pot. Will this solve itself?

Longer story, we've moved into an older house. We noticed peeling paint and room suffering from cold and high humidity. We've replaced the windows because they were shot. The humidity situation is improving week on week. Nevertheless I got a damp detector and started investigating the room. I am able to localise specifically damp to the location where the chimney runs. It's a twin flu for a now long since gone fire in the bedroom. The bedroom flu has a cap on it with small holes for venting.

Downstairs the fireplace is still in play and has a gas fire. The gas fire was out of commission but it is now back working again as of yesterday. The gasman also fitted a cowel to the top of the chimney to prevent water ingress.

Now when I run the fire I can feel the warmth in the wall where the chimney runs. OK maybe not warmth but it's warmer than the surrounding wall surfaces.

My question is this, will this damp now dry out?