Liz Buchanan BVSc MRCVS
Hello - and no wonder your dog is licking at this. The claw is the equivalent of your finger nail and we all know how irritating it is when even those little strips of skin at the sides of the nail bed peel back. This picture is blurred and I can't see the position of the nail or its bed, but from what you say it must be sore and sensitive. Licking is a sign of pain and looks to be damaging the skin - it may also have introduced infection. Preventing the licking and not treating any pain or infection, may be unlikely to solve the problem. The sore area may be spreading outwards.
This may need antibiosis to help it heal and real and effective pain relief, as well as either a covering or a buster collar (your vet will examine the area and weigh the situation up depending on the specifics - air to the wound can be helpful - and help you to decide).
I know that it only seems a small thing, but these can quickly become a much bigger thing if unchecked and asking your vet for advice really will prove the best next step.
In rare circumstances I have also seen other diseases, including various cancers, present like this, so it is a good idea to get to the bottom of it sooner rather than later, just in case.