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They made a mobile phone game for the 50th anniversary called trexels. You pick your own crew, build your own ship, and do missions that play out like episodes of star trek. Your crew get experience and can level up and then you distribute skill points.
It does have the cash grab model that all mobile games use these days (which kinda takes away from it imo) but it's mainly used to speed up the progress of the game. You can get all the paid stuff just from playing the game by grinding out and saving up the dilithium crystals. Which leads me to believe the cash grab model was CBS's idea and not the developers (cause CBS are a bunch of slimy fat cats who only care about $$$).
It's a really good game for killing time and I highly recommend it. Android
Try Star Trek Trexels very fun game