Arda Guler should leave Real Madrid, he cannot be a starter in this team. There are too many big name players in Real Madrid that cannot be benched for him to play. Even if they have bad performances, they will still start in the next game. Real Madrid is a big club and Arsa may want to take his chances there and fight for his spot. I think Arda can decide what’s best for himself.
He was never going to be a starter there, he knew about it t before he signed the contract, he's only a prosper and not a crucial member of the team. The best solution would be to go on loan for to mid table team with less pressure to get more playing time to help his development. He's not going to achieve that on the bench week in, weeks out.
Arda Guler is seen as the future of Real Madrid. And just as you said he is aware that he needs to be patient. Karim Benzema had to wait until Cristiano Ronaldo left Real Madrid before he began to feature consistently or enjoy first team shirt in Real Madrid.
I have read several sports news where Turkish fans are complaining about the young player's minimal use in Real Madrid. They felt that their golden star should always feature in all games. Arda's time in Real has not come, he will continue to be a backup player until he matures or gets the opportunity. He would have gotten more playing time this season if not for the signing of Mbappe.
Carlo Ancelotti will keep on using him his main strikers are injured, suffer fatigue or are in unimportant games. But I know that the Turkish player is happy to be part of the biggest club in Europe. But he is not, he could push for a loan deal because I don't think that the club will let him leave permanently.