This should be fixable with a good touch up product. A good touch up product should have a filler and finish combined in it so can be sued for this sort of repair.
You can use the touch up product to fill any of the little cut areas and this will act like an adhesive, use very small amounts of product on something like a dental tool and then using the same tool press the leather back into place and this should seal the cuts. You will need to have a colour mixed to match your leather otherwise the repair will look worse than the damage. Use as little product as you can. Do not be tempted to use fillers and glues on this sort of repair as they are not necessary and if not used correctly could make the repair unfixable.
With touch up products it is not necessary to finish over the top but on high wear areas we would always advise you to do this.
Hope this helps