Clive Hugh said:
Good answer.
Really, bring it to a pro. Just regluing it will probably fail very quickly (at least with body binding), as you are not fixing the core problem. The thing is, that old cellulose binding shrinks with time (be glad, it rarely suffers from spontainious combustion in the sizes we use for binding; large sheets of it which get used for pickguards can do that sometimes). It takes a lot of clamping to get it back in there, and even then it is usually a one to ten year job. But the cauls involved in doing it right are very high skill woodworking, and you don't want to mess with that.
The perminant fix, which does not look very good, is to cut the binding and piece in a new section of binding, which will never match perfectly.
And of course, if it is the fingerboard binding on a Gibson, well now you know a little bit of why people give Gibson a hard time about their workmanship. That is usually a simple glue failure, and while I would still encourage you to take it to a repair shop, you can get by with some Duco Plastic Cement, and use strips of masking tape to clamp it in place. But be VERY careful not to let any of that Duco get on the finish, as it will eat right through, and then you have a whole other issue which will cost about 10 times as much to fix as bringing it to a good repair shop in the first place.
Light
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M.K. Gandhi