As a Turkish person, even though he played for our opponents, Arda Guler is way too talented to give up this easily. I understand that there are some players at Real Madrid which makes him not get full minutes, and of course he can go to a worse team and play every single game, but that doesn't mean that he will improve the same. The reality is, we could see Arda still be a big part of that team, he is too young, he is 19 years old, and we can see him for a few more seasons, maybe like 2.5 more seasons and then be a started, we don't know if he will be better than the ones they have or not. I believe he can be, and that's why he should stay and play whenever given chance and he does play a lot recently because of injuries as well. If he stays a bit more, and play, after 2.5 seasons, if he still doesn't have the minutes then he can leave, but right now would be way too early.
It can be a smart move to leave Real Madrid for a while. These years are key to a player's development and if he is mostly spending his time sitting on the bench, I think it doesn't mean to give up if there is a club seriously interested in him. I agree that he shouldn't move to a really bad club, but it is not black or white. Leaving Real Madrid when he can still play in the Champions League would probably be the best he can do. He can thrive elsewhere, already has some good experience and might be a viable player for so many other clubs.
But for now I don't think he has what it takes to become a starter anytime soon or at least it will not be easy. It's a bit of a gamble to stay there if that means he will remain a substitution player for too long.