Hi
This is such a hard question to answer really effectively. So much depends on where you are now, how many hours of training you are going to do, where, what is available to you, where you were when you left, what skills you are going to be doing/learning etc.. There is no magic answer like 20chin ups x 2 sets a week. This is rubbish. Not to mention that chin-ups i think are wayyyy overdone in gymnastics.
What i would do if i were you is ask your coach to write you a basic off-season conditioning program. It should consist of about 70% general conditioning exercise and 30% specific (such as cast to HS).
Exercise that should be included are:
Upper Body
Chin-ups, Handstand push ups or variations (if you can't be spotted), Shoulder shrugs, Press to HS, Rope climbs etc... Dips or Push-ups
Mid section
The list here can be HUGE, but the least, leg-raises, planche rocks, and planche lever ups, hollow holds and variations, arch holds and variations, side holds, wall bar levers etc..
Lower body
Drop squats, Drop jumps, sprints with reisistance, Heel drives, calf raises
Specific conditioning
cast to HS, layouts (front), standing back tucks or pike, snap downs, etc..
I mean this list on lists some of the basics general and specific exercise. There is no point in giving you numbers because i dont know what you can do, and how you do it. For example with the layouts (front) saying 10 layouts might be rediculous if you can only do about 2 good ones. Or saying 10 cast to HS might be to easy. You see what i mean, i just don't know where you are at to be able to adjust the intensity and volume of your workouts so that you are working efficiently and effectively.
You coach should be the one to prescribe you the conditioning. One thing that is universal is. If you are doing powerfull explosive work you need to rest between 3-5min per set, and no more then 30sec per rep. Endurance work (such as abdominals) long holds is good, lots of reps little rest. Hypertrophy is reps of about 10-15 (reaching failure on last rep) rests about 2min. When you can do something for more then 10 reps and explosively, increase the resistance, slowly so that you can continue working fast, but against resistance.
As you approach the compeititon season and you start working on fixing up skills and what not your coditioning should shift from general to more and more specific.
I know that this is probably not the answer you were hopping for, but anything else will be just generalized answers. Its like saying just by following this recipe you will be able make the dish in the picture 9/10 times it doesn't look anything like it, or taste like it.
Good luck and work with your coach. If he knows what he is doing he will be your best help. Once you have a program post it if you wish for analysis and comments.