hi, I know agonist muscles are important. But I don’t currently owns bench for chest workouts. I’m current log 5’7 153 lb and can do probably a set of 7 pull ups to failure max. And 2 “archer “ variation pull ups. I only do push ups for pec work.
To answer your question: Plenty. You don't need to work on push ups, deadlifts, squats or bench press to get better at pull ups, that’s BS. You need to do pull ups to get better at pull ups.
If what you're interested in is getting more reps, you should look to slowly increase you total volume, look up grease the groove, pyramid sets. Different variations like weighted, different grips and isometric holds might make sense at some point, but if you can only do 7, just focus on slowly upping your total volume without coming too close to failure. Let's say you work on your pull ups 3 times a week:
Week 1, Day 1: 1-2-3-2-1. 9 total reps. Day 2: 1-2-4-2-1. Day 3: 2-2-4-2-1. Week 2, day 1: 2-2-4-2-2, etc, etc, etc. Have a rest period between sets of something like 1-2'. When this stops working (meaning, you are failing sets or grinding constantly), maybe add an extra set or 2 (so imagine that in week 6 it might look like 1-2-3-5-3-2-1). Also, give yourself a couple days of rest after a few weeks and re-test your rep max when you're fresh to track your progress. After a while progress from session to session won't happen, and you'll have to plan your progress week to week, and maybe work some lighter days into the week, but that's for later.
That's just an example, but it would be a decent start. With time, when you can do 12-15+ you can work some variations in, depending on whether your goals are centered on high rep counts or more heavy lifting. If you're interested in muscle ups, it would probably make some sense to work on dips eventually as well. Good website for bodyweight/bar skills:
http://www.beastskills.com/tutorials/