In reply to davidbeynon:
Yay, this is when I get to share my secret weapon!
In my experience, hips and hamstrings (the areas you need to work) respond especially well to stretches held for a slightly longer duration (think a couple of minutes rather than the more usual 30-60 seconds).
Because they're often sitting poses, they are also ideally suited to doing while watching TV. I owe my front splits to a box set of The Wire watched on my laptop on the floor, basically. I am not making this up.
So pick a few stretches, and get in the habit of doing them *after* climbing or any other form of exercise you do, when you're well-warmed up. And also get on the floor and do them whenever you watch TV (or listen to podcasts, or whatever).
In "9 out of 10 Climbers", Dave MacLeod says he thinks the following two are the crucial ones for climbers (links go to pages that have decent pictures, as "9 out of 10" doesn't have illustrations of them):
https://www.ekhartyoga.com/more-yoga/yoga-poses/wide-angle-seated-forward-b...
https://www.yogajournal.com/poses/bound-angle-pose
Just go to the point where you feel a gentle stretch (definitely don't do anything that hurts), then hang out there for a bit, watch TV, and remember to breathe.
If you want a few more, I'd suggest trying some of these, and seeing what suits you, and what feels like you can get a good stretch out of it:
http://www.yogabasics.com/asana/half-wind-relieving-pose/ (I'm not making it up, that's what it's called)
http://www.yogabasics.com/asana/seated-head-to-knee/ (don't panic, just lean forwards as far as you can to get a gentle stretch)
https://www.yogajournal.com/poses/reclining-big-toe-pose
https://www.yogajournal.com/poses/downward-facing-dog -- less suitable for long holds, but it's good for your shoulders, good for hamstrings, good for your back, good for your calves; it is the bomb
As MacLeod points out, though, as well as passive flexibility, you also have to have active flexibility (what some trainers call "mobility") -- the ability to move your body part into that position without assistance. Sometimes grabbing your foot and pulling it onto a high hold can work in a pinch, but it's obviously better if you dont have to. *g*
A nice exercise for this kind of thing is pulling your knee in towards your chest while standing on the other leg (a standing version of wind-relieving pose, basically).
Holding it there with your hands for a bit is another nice hip stretch (and balance exercise); but if you then let go with your hands but try to keep your leg in the same position for a bit, it starts building strength and muscle control.
As you improve your flexibility, you can start trying the same thing with a straight leg.
If you get into all of this, there are fantastic resources for beginning yoga out there (lots of free video podcast classes and so on), and lots of people find that yoga does complement climbing very nicely.
But just picking a few poses to work on and doing them a lot will give you a huge amount of bang for your buck.