On July 27, 2019, Dest made his debut for the Ajax first team in an official game, when he started the 2019 Johan Cruyff Shield match, against rivals PSV Eindhoven. Ajax won the match, 2–0, and in consequence, the title. On August 10, 2019, Dest debuted in the Eredivisie, replacing Noussair Mazraoui in the 54th minute of the Ajax 5–0 home win against FC Emmen. He also appeared as a substitute in qualifying matches for the UEFA Champions League against PAOK and APOEL. In September, Dest was officially promoted to the Ajax first-team squad. On September 17, 2019, he made his first start in the Champions League against Lille OSC; a match which Ajax won 3–0. Dest finished his first senior season with 35 appearances in which he scored two goals—both in the KNVB Cup fixture against Telstar.