The pull-up improves grip strength, but add an isometric hold at the end of a set and you'll blow up your grip strength while sparing your elbows and shoulders.
Loaded Hang Iso-Hold
Do the iso-hold at the bottom position of the last rep of a set of pull-ups. This is one of the simplest ways to challenge grip strength and endurance from an overhead shoulder position.
You can do it with any hand position: supinated, neutral, or pronated grip. I prefer the fully pronated (overhand) grip with a medium width between hands. This position is the most natural.
Control the descent of your last rep on the pull-up bar and maintain the tension and the position at the shoulder while squeezing the bar as hard as you can. Stay in that position, fighting the urge to go lax at the shoulders. Don't hang out on the capsule and ligaments.
If you want to take your full body strength to the next level, assume a hollow body position with your legs straight and slightly flexed at the hips to engage more of the anterior core. From here, hold as long as you can.
Do this on your last working set in every workout and your grip will develop, your shoulder mobility will improve, and your pull-ups will feel easier. It's a great way to self-treat cranky shoulders, too.