The England international missed several weeks of the season injured, but completed both of Madrid's last two matches.
Alexander-Arnold, 27, was rotated with veteran Dani Carvajal at the start of the season before his hamstring injury.
"I think we will see a better Trent," Alonso told a news conference before Madrid's LaLiga clash with Girona on Sunday.
"Without doubt, it's positive after the injury, he could do 90 minutes against Elche, 90 against Olympiacos.
"We need him. It's his first year, and it's normal to have this adaptation (period)."
The defender left his boyhood club, Liverpool, after playing more than 300 times for the Premier League giants.
Alexander-Arnold struggled at times in the 2-2 draw against Elche but found a higher gear as Madrid beat Olympiacos 4-3 in Athens.
"He's starting to feel (like) himself," continued Alonso.
"He is demanding too; he plays at a top, top level. We have to be there for him, in this change that is so big for him, but it's good news."
Alonso also praised another England international, Jude Bellingham, after his recent good form.
"I have very good communication with Jude, a very good relationship," said Alonso.
"He's a top world-class star, but he has this desire to improve, to learn, to be more efficient with the big potential he's got.
"I like these players with this curiosity and initiative to ask what we can do better."
Madrid have drawn their last two league games and will look to build momentum again against Girona.
Alonso confirmed Franco Mastantuono, Antonio Rudiger and Eder Militao were back from injury and will be part of the squad, while Raul Asencio was a doubt.