Didn't mention what kind of tang. If it's a cylinder, you're in the classic differential contraction problem. Wood expands/contracts at different rates on quarter and face grains as humidity changes, and the steel not at all. If there's a real ferrule, which is to say a substantial metal ring on a tapered shank, you might just be able to get all you want by tapping it down. If not, remove, coat with adhesive and return the entire steel part to the hole in the wood. Doesn't really matter what the adhesive is, since you're not using it as glue, just as a space filler.
If it's a non-cylinder, dollars to donuts it's tapered, so a couple of quick raps on the opposite end will tighten in the socket, and a tap or two on the ferrule as a followup probably won't even be needed.
