Tamm joined the youth system at
Nõmme Kalju at the age of five years-old. He won the Estonian championship with Kalju in 2018, and also won the Estonian Super Cup that year. Tamm scored Kalju's winning goal in their 1–0
UEFA Europa League win against
Stjarnan in 2018. He played in 25 games and scored two goals in the Premium League prior to August 2019, when he joined
Grasshopper Club Zurich in Switzerland, on a one-year loan-deal, as part of an exchange deal that saw
Max Mata move to Kalju, with Tamm linking up with the Grasshoppers under-21 side. After retuning to Kalju, he scored 28 goals during the
2024 season, putting him in the running for the
European Golden Shoe. Following the end of his contract, in January 2025 he signed for
Slovenian PrvaLiga club
Olimpija Ljubljana on a free transfer. He scored 8 minutes into his debut match in a 5–0 win against
DNŠ Ajdovščina, on 2 February 2025. He also scored and was credited with an assist in his second match, against
FC Koper. In January 2026, Tamm signed for Scottish side
Livingston on loan until the end of the 2025–2026 season. ==International career==