Are you replacing a leather wrap with a leather wrap? Or are you replacing a 'sport grip' that feels like rubber on a golf club? either way, measure how thick the original was and then the new one to find how much you need to build or reduce by. Remember, it is a round object, so say if the original wrap material measures at .045" thick, and your new leather is .025" thick, then you need to build the overall thickness of the handle by .020" per side, or .040" finished overall dia., so go bigger and sand/machine it down. How off it is dictates what method is needed to build it up by. If you need to build it up by .025 + I would use veneer first, then sand to what is needed. If only .010", then a couple coats of 5 minute epoxy. I have not used linen under a leather wrap, so no idea how that would work long term. You may also be able to replace with a thicker piece of leather. Depending what you use to build it up with, it can introduce other problems a month or 2 down the road also....masking tape or other linen or fiber based options need to be pressed down as far as possible before installing the final wrap, otherwise it may seem fine at first, then as time goes by and the hand presses it down further, now you may have a ridge you didn't anticipate. .... even using epoxy will shrink a little down the road........ALSO don't use any material to build it up with that your contact cement will melt when you apply it....found that out the hard way.
I use a UV cured solution when I need to build it up only a small amount, as once it's cured....no shrink, and hard as nails, so the feedback comes thru as usual...otherwise, I use a veneer solution and go from there. ...HTHS
Dave