Tree gear vs. Pole gear.
I am new to this site, but I was taught how to climb and trim by one of the best in the midwest, working for the city of Milw. I now work for an electric utility and spent the better part of 16 years climbing poles. The advise you have been given is right on. You need to trade the pole belt for a saddle and the gaffs are also probably going to be too short for tree work. Pick up a good arborist manual to give you the basics. Anything by Alex Shigo also will help you understand how a tree grows and then how to trim it.
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These guys are right. Go to the websites of Bailey's, WesSpur, and Sherrill. They all sell the basic equipment you will need in kit form. If you have a good arborist supplier near you, go in and try some saddles. The saddle is very important. It must fit just right, and be comfortable to support your entire weight for long periods of time. You can spend a fortune on ropes and equipment, but to start off, you need a good rope, good saddle, some good boots (not the kind made for gaffs or spurs), a couple of locking carabiners (don't take any shortcuts here, buy the "three-way" kind that need three separate moves to open), and a lanyard or flipline. Steel-core or non steel-core, it doesn't matter, unless you are climbing near electric lines, which you shouldn't be doing anyway, until you learn more.
You'll also need a throwline, throw weight, and a bag. Gotta get the rope up there. Also, a helmet and some good gloves. I'm not kidding.
Finally, get
The Tree Climber's Companion, the best $20 you ever spent. Read it cover to cover, more than once. All the catalogs have it.
Learn the knots, and practice with the rope over a branch maybe 10' off the ground. Make sure everything works. If you fall on your butt from maybe 12", you won't get killed.
Then, most important - find somebody who climbs for a living and is willing to show you how it's done. You can't learn it from a book, but the book sure helps.
The stuff you got is OK for climbing utility poles. You don't use gaffs on a tree unless you are going to take it down. You should be able to sell the stuff if you don't plan to pole climb later.
Climbing is great fun. I don't climb for a living, but I wanted to learn how. Just be careful and take it slow.
Good luck, man. Have fun and stay safe!