Everyone has pretty much hit the nail on the head but here's a few tips anyways (All advice is from my subjective experience) :
1. Practice Slow, clean & controlled - Whatever you want to play quickly, you want to be able to play it cleanly (I.e no unwanted string noise/sloppiness). The best way that I've found to get this to fruition is to take the thing you want to speed up and look at all it's small moving parts when slow. Make sure you could play the lick at less than half speed, confidently and without mistakes. If you don't feel 100% in control of what you're doing, it's not the right time to play it fast.
2. Push in slightly harder when practicing slow -
This is something that I found fast tracked certain licks for me. The way I make sense of it is this: If you put in 200% strength slow, then when you play fast, you can ease up completely and still hit the 100% strength needed to fret every note. Fast playing should be relaxed/controlled.
3. Don't go fast too early -
Most, if not all Guitar players that are interested in more technical styles have what I like to call the 'inner speed gollum' that just wants to play at full speed *now* I am living proof of this
You're practicing away and you feel the lick *click* a bit and you think (This is my time - full speed - ...aand it falls apart) - try to recognise this compulsion when it manifests and squash it. Most things require a gradual speed up process. This step will stop any undue tension in your playing at a high speed and save you any frustrations.
4. Weirdly - try not to get too hung up on your speed BPM -
This may seem counterproductive, but worrying about how fast you can play can strangely inhibit how fast you can play in the long run. The reason (at least from my own experience) Is that you get into a mindset of I'll respect my chops/have worth as a player when I get to *this* speed - and you start pushing too hard into that/basing your worth off of the results. For me personally it bred a lot of frustrated, negative practice sessions and hoenstly time wasted trying to strain to the point that I was only going to arrive at patiently, in my own time - not saying this would happen to you or that you would think this way, but it's a mindset I'd definitely watch out for - it creeps in!
I tend to write loads in response to speed posts because I remember the frustration myself - take your time and enjoy the process. Patience and persistence will convert to progress - just dont put a date on it !