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The England star moved to Los Blancos at the start of Juneafter they forked out £10million to secure his services from Liverpool.
At first, the 26-year-old was going to move to the Spanish giants on a free transfer, but Real's eagerness to include him in their Club World Cup squad saw them pay the eight-figure fee to sign him a month early.
He played the entire match of Real's 3-0 victory over RB Salzburg in their final group match, the first time he has done so since joining Xabi Alonso's side.
It's about kicking on and being the best player that I can be and giving the best for the team and helping the team win as many games as possible starting with this competition."
The defender lifted two Premier League titles, the Champions League, the FA Cup, the Club World Cup (in its previous format) and two League Cups at Liverpool.
He also notched a remarkable 67 assists during his time at Anfield, a Premier League record for a defender.
Alexander-Arnold made a positive impression on his team-mates and fans by speaking in Spanish at his unveiling.
You work hard to try and understand what people are saying and be a part of it.
"But the manager speaks to me a lot individually to make sure I understand everything that gets said.
They will next face Juventus, who suffered a 5-2 defeat at the hands of Manchester City in their final group match, on 1 July.
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