Prince of Persia: The Forgotten Sands
For starters, it would actually have something to do with The Sands of Time trilogy outside of just have the same Prince and a couple references. It was a decent idea to place it into the five year break between The Sands of Time and Warrior Within, but also trying to make it a remake not only made it feel more disconnected from the events of the past games and made it feel like a cash-in but it also left the story opening up more plot holes than closing. For instance, they sort of imply that the medallion The Prince has in Warrior Within came from a relic he found in The Forgotten Sands, but that makes absolutely no sense when it is clear the medallion in Warrior Within has connections to The Island of Time, something that the relic in The Forgotten Sands has absolutely no connection to. Personally, I would make the story actually be able The Prince's decent into his hardened state during Warrior Within and actually make it about everything he endured from The Dahaka during that period.
Also, I would make the combat more like the older games but just allow the powers to give it more depth, similar to how the powers functioned to add more to the platforming and puzzles. From a gameplay perspective, the combat was by far the worst aspect of it, and the game actually would have been much better than just average if they had actually given us a decent combat system like the old games.