After one goal in twenty-two matches for Gimnasia y Esgrima, Alderete completed a transfer to Huracán at the conclusion of his loan spell.[2]
On 4 June 2019, Alderete agreed a move to Swiss Super League outfit Basel; with the deal officially going through on 11 June.[7] Alderete joined Basel's first team for their 2019–20 FC Basel season under head coach Marcel Koller. After playing in five test games, Alderete played his domestic league debut for the club in the away game in the Stade Tourbillon on 19 July 2019 as Basel won 4–1 against FC Sion.[8] He scored his first goal for his team four days later, on 23 July 2019, in the away game in the Philips Stadion in the second qualifying round of the 2019–20 UEFA Champions League. But this could not help the team, as Basel were defeated 2–3 by PSV Eindhoven, who scored two goals in the last minutes of the game.[9]
Alderete left the club during the transfer window of the next season. During his short period with the club Alderete played a total of 64 games for Basel scoring a total of four goals. 31 of these games were in the Swiss Super League, six in the Swiss Cup, four in the Champions League, 13 in the Europa League and 10 were friendly games. He scored two goals in the domestic league, one in the Swiss Cup and one in the Champions League.[10]
Hertha BSC
On 5 October 2020, Alderete signed a long-term deal with Hertha BSC.[11] He made his debut in a 2–1 debut at the Red Bull Arena against RB Leipzig on 24 October.[2] On 12 July 2021, Alderete signed with Valencia CF on a season-long loan with the option to buy.[12]
Getafe
On 19 August 2022, Alderete joined Getafe on loan with an option to buy.[13] On 25 May of the following year, he signed a permanent five-year contract with the club.[14]
Sunderland
On 12 August 2025, Premier League side Sunderland announced the signing of Alderete on a four-year contract for an undisclosed fee.[15] On 27 September, he scored his first goal for the club in a 1–0 away victory over Nottingham Forest in the Premier League.
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