I just started my gelding on pole bending this past week. What could I do to getting his end turns tighter and faster?

Take your time. When training for speed events such as barrels and poles it's best to start slow, get the fundamentals down. 110% and then being to add speed. Start wit walking and trotting the pattern without any mistakes. If your hirse develops any bad habits while training the take a step back and take the time to fix them
I'd look into a Pessoa lunging system. They're designed to engage the hind end and get the horse balanced with a supple topline and their hind underneath them.
Go slow, and make a 'wide' pattern through the poles. As soon as your horse's shoulder is even with the pole, start moving him off your leg over for the next pole. Go wider than you need. You'll come in wide to your end turn, and that will set you up to come out close, setting you up for the next pole. I ride two handed all the way through the poles, I never drop my outside rein. Make sure you're sitting in the turn, and give leg all the way through the turn (squeeze). Slow is going to get you to fast and consistent fast way quicker than hurrying through the pattern in the beginning.
trying circling, you can do some spiraling work on the circle..( big circle then keep circling going inward/spiraling) you can also do hillwork to help make his hind end stronger which will help.. also transitions
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