Alexander-Arnold has just joined the team and has already missed the Club World Cup final due to injury. I don't know how serious his injury is, I think it was just a bruise, but Carvajal is also not ready to play from the start yet, so Real Madrid still have a lot of questions regarding their defense. Although there is still time before the start of the new season and their situation is still better, because the defenders are already training with the team.
Arnold is not going for a long time, he will resume the season with his team while Carvajal joins them probably along the line. Having two Right backs means they are settled in that area, both center backs really caused them issue during the match against PSG, it didn't change a thing because Rudiger has always been an outstanding player, won't judge him out of one big mistake, along the other pair Militao, Asencio are still remarkable to cover up the gap. Real Madrid needs to work with their performance, buying of players won't help them form standard if they don't understand and adapt as a team when playing.
Trent Alexander Arnold is actually a very high-quality player. He played some fantastic matches with Liverpool. He spent a significant part of his career with a successful Premier League team. He most recently won the title with Liverpool. I believe he can deliver a similar performance at Real Madrid once he overcomes his adaptation issues. Spain is as good a league as the Premier League, and Trent would fit in easily there.