The reins I am using are plain leather. The problem is that they are very slippery and wearing gloves makes it worse. I am ok at the walk and trot but at the canter is where I have the problem. My horse is green and will pull at the reins to try and slide them though my hands as she would like to go for a good gallop and I’m sue bucking would also ensue if she thought she was in charge. I end up gripping the reins very strongly and she is still able to get an inch or more to pull through my hands before I have to bring her down to the trot. This is obviously not a good situation. I am not able to switch to different reins. So I am asking what I can do to make the leather sticker so she can’t pull them through my hands so easily and so I don’t have to grip them so strongly.
Sounds like you need different gloves!
Otherwise you could use one of these products:
https://www.smartpakequine.com/pt/sekurgrip-229
I’ve used them on my breeches to help on the, uh, “fresher” horses 
But I’m sure they would work on reins. (I would recommend the sekur-grip instead of the spray).
Otherwise you could just get web reins - you can get some cheap ones until the pulling/slipping isn’t an issue 
I agree with the suggestion to try some different gloves. In my experience, synthetic suede palms are great (and relatively inexpensive). I personally swear by Noble Outfitters “Perfect Fit” gloves. They get even stickier when I sweat!
https://shop.doversaddlery.com/perfect-fit-glove/p/X1-39134B/
I’m not sure why you can’t switch to different reins? Are you borrowing a someone else’s bridle? If that’s the case, I think any product you could put on reins to make them stickier might change the look of the leather and/or annoy the person who prefers the smooth leather reins.
Also, you can get leather reins with stops. I have these.
https://www.horze.com/reins/horze-laelia-reins-with-stoppers/10703.html?color=BL
Oh! And I just remembered several Very Important Points about holding the reins… you say you feel like you have to “grip too strongly”. Based on my own experience with a sneaky rooting horse, I’ve learned to really pay attention to hand position. And rider position
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Thumb on top! (I know, obvious, right?) But are they always? Or are you like me and tend to rotate your hands inward so your knuckles roll up instead? My instructor likes to remind me “not to spill my wine” - that works for me.
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Most of the pressure on your rein needs to come from your thumb pressing against your index finger. That leaves the rest of your fingers loose to provide more subtle cues
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Really think about your position in the saddle. Check your core. I visualize anchoring my reins into my shoulders, and my elbows are those rubber donuts on side reins. You can give a little, but you are still setting boundaries. If you are solid, your horse will have a tough time yanking you out of position.
I’m also confused why you can’t use different reins? Even if it isn’t your bridle, just buy your own pair of reins and change them out when you ride. It takes like 2 minutes to change reins.
I prefer braided leather reins, myself. My instructor thinks rubber are less slippery.
Those Noble Outfitter’s gloves linked above are wonderful.
I have tendonitis in my right hand from work which keeps me from being able to hold the reins well, and agree about gloves and rubber reins.
For me, thicker reins are also easier to hold since at times my fingers physically don’t close all the way, thus I go with thick rubber reins though there are thinner options out there.
My gelding went through a root and take off bucking phase. I literally wrapped the reins, and even my trainer did, because it was simply too dangerous to let him possibly get the reins from us. We made sure to keep him on or above the bit, never below/behind for safety through that whole phase, too. It’s a healthy place for a young horse to be, so I’d suggest you consider that as well - that you are sure you’re riding a young horse up and open.
Yeah - switch out the reins. Braided, rubber-lined, or (my favorite) leather with rein stops. Also, some of the web reins are much less sticky. I happen to dislike them, but they are inexpensive and work just fine. (I’m a snob. If it ain’t leather, it ain’t going on my horse!)
I have pretty damp hands when riding which makes for slippery reins. These reins were a game changer! They are also super soft and comfortable to hold. I ended up buying a pair for my mom I love them so much. You can find them in Canada and the US. I bought one pair in Germany while visiting, they are a little cheaper there.
http://www.sprucewoodtack.com/schockemohle-dura-soft-leather-reins-with-nylon-inlay.html
Can I ask how wide they are? I bought a pair with rubber on the inside from Schockemohle, and they were to wide for my hands…
Calf lined reins with “indents” instead of raised stops are the reins I like. Red Barn makes them, as does Arc D’Triomphe, and others, I’m sure. Mine are 5/8", from Red Barn/KL Select.
Not wide, actually more average to narrow I would say. I don’t actually know how wide they are. They are slightly thicker than plain reins as they are wrapped. Sorry, that probably didn’t help 
