contact cement ...
David Weaver
which is barge, right? sand the pad of the holdfast if needed and give it adequate time to dry.
I use "shoe goo" to hold on two aluminum angle pieces in my metal vise and then often tighten things to "lifting a 400 pound bench" end off of the ground to get the vise loose sometimes. The glue surface between the two isn't exactly ideal and I generally haven't had to refresh the glue more than once a year.
If the piece does ever come loose from the hold fast, it'll take a minute to re-apply two of them.
Same with the face of my wood vise - just shoe goo.
But I've never had any type of strop come loose even though I oil mine heavily. The only issue I've ever had is leather that's porous using titebond - if the glue makes its way most of the way through the strop, there will be hard spots. I did this with old junk leather and the only fix for that is the garbage can.
That's my only warning - if the glue is a type that will soak into leather deeply (like a water based glue) don't use so much that you end up glue sizing the leather into a solid block.