Clair didn't become a Claymore for the same reasons mosst of the others did.
She did it for revenge. That may be her strength. The other Claymore's all have special skills they hone, but Clair really didn't until later, when she learned she could develop them.
In a way, her skill was "learning" from others, in order to improve her own skills, which the other Claymore's can't do, they can only improve their current abililty, not develop new ones.
She was honing her skills and learning to improve them with one goal only: to kill Priscilla.
The other Claymore's were more like "athletes" who competed with each other to see who is the best. Clair really didn't care about any of that.