Alaba's injury is considered quite serious, with a torn anterior cruciate ligament in his left knee, and he will undergo surgery in the coming days. This is an extremely heavy loss for Real Madrid as a torn ACL is the worst injury for an athlete. Alaba is expected to be out for 7-9 months, and the season is practically over for him from this December.
ACL injury sucks and Alaba is considered as Out of Season.
https://www.sportsgambler.com/injuries/football/spain-la-liga/The absence of Alaba, I believe, will seriously affect Real Madrid's plans for the remainder of the season. He is currently the team's primary left-center back, pairing with Antonio Rudiger after Militao's long-term absence. Now, with Alaba's injury, Real Madrid has only two central defenders in the first team, Nacho and Rudiger. This is a thin squad, especially as they approach important matches in early 2024, such as facing Atletico Madrid twice in the Spanish Super Cup and playing against the league leaders Girona (February 11), not to mention the Round of 16 in the Champions League.
They have limited players for their central defender positions and with their busy schedule by playing in both Champions League and La Liga, fighting for titles in both competitions, Real Madrid will have to look at the transfer market in January to find a temporary replacement for Alaba. The replacement player can come to Real Madrid with a loan or a paid transfer but they will not want to spend too lucrative transfer fee for it and even can not convince other big clubs to let their world class central defender out.
It's likely that midfielder Aurelien Tchouameni will play as a center back in place of Alaba. Therefore, Real Madrid is likely to consider finding a replacement in the January transfer window to strengthen the defensive line.
If I am not wrong, Tchouameni is a defensive midfielder and he has never been used as a central defender.