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first check that none of the coils of the hairspring are touching each other while moving, or touching the balance cock. This shortens the effective length of the hairspring and will make the watch run fast. If that looks ok then check the escapement, make sure the escape wheel is moving evenly through the pallets, if you see any “skipping” this will show the “depthing” is not correct.
How much is it gaining per day?
If the hairspring is the “pinned in” type then this may be adjusted but check the other things first.
Good luck and let us know what you find.