Tamm started out playing for hometown team Tulevik. He made his debut in the Meistriliiga on 29 March 2008, in a 1–1 home draw against Sillamäe Kalev.
Flora
In February 2009, Tamm moved to Flora. He scored his first Meistriliiga goal on 9 May 2009, in a 4–0 away victory over Tammeka.
In August 2009, Tamm joined Italian club Sampdoria on a season-long loan, where he played for the club's Primavera side.[2]
Tamm returned to Flora in August 2010. He helped the team win the Meistriliiga in 2010.[3]
IFK Norrköping
On 27 December 2010, Tamm signed a three-year contract with Allsvenskan club IFK Norrköping, with the option to extend the contract for another year.[4] In July 2011, he moved to Division 1 side IF Sylvia on loan. Tamm scored on his debut for the club on 9 July 2011, in a 2–1 away victory over Motala AIF. He made his debut in the Allsvenskan on 25 August 2011, in a 2–1 home victory over Djurgårdens IF.[5]
Trelleborgs FF
On 2 December 2013, Tamm signed a one-year contract with Division 1 club Trelleborgs FF.[6]
Return to Tulevik
On 9 February 2015, Tamm returned to his boyhood club, Tulevik, on a one-year contract.[7] Positioned as a centre-forward, he went on to score 9 goals in 15 league appearances. On 2 May 2015, in the season 2015 he scored a Hat-tricks against Paide Linnameeskond.[8]
Return to Flora
On 22 June 2015, Tamm joined his former club Flora for an undisclosed fee.[9][10] He went on to help Flora win Meistriliiga titles in the 2015 and 2017 seasons.[11][12]
Various loans
On 31 January 2018, Tamm joined Eliteserien club Sarpsborg 08 on a season-long loan.[13] Starting from the first qualifying round, he helped the team reach the UEFA Europa League group stage. Tamm played in all six group stage matches as Sarpsborg 08 finished last in their group.
On 27 June 2019, Tamm moved to Eliteserien club Lillestrøm on loan until the end of the 2018–19 season, with the option to make the deal permanent.[15]
On 10 July 2022, Tamm signed for Romanian Liga I club FCSB.[29] On 24 July 2022, he made his debut in Liga I against Rapid București at the Stadionul Rapid-Giulești in Giulești. He scored his first goal for the club in a league match against Craiova on 31 July.[30] He was later chosen for the league's Team of the Week.[31] On 3 August he scored his first goal in the UEFA Europa Conference League against DAC Dunajská Streda at the MOL Aréna in Dunajská Streda providing the 1–0 away victory for his team.[32] On 14 August he scored the winning goal in a league game against Chindia Targoviste and again was named to the Team of the Week.[33]
Botev Plovdiv
In July 2023, Tamm signed a contract with Bulgarian club Botev Plovdiv.[34]
International career
Tamm has represented Estonia at all levels, from the under-16 side to senior squad. He represented Estonia's under-17 team at the 2008 Under-17 Baltic Cup, eventually reaching the final.[35] On 10 June 2011, he was named by manager Tarmo Rüütli to the Estonian senior squad to face Chile and Uruguay in friendly matches.[36] He made his senior debut for the on 19 June in a 4–0 away defeat to Chile.[37] Tamm scored his first international goals on 7 October 2017, when he scored a second-half hat trick in a 6–0 away victory over Gibraltar in 2018 FIFA World Cup qualification. In doing so, he became the first player to score a hat-trick for Estonia since 1996.[38] He won the 2020 Baltic Cup with Estonia, playing in the final against Lithuania.[39] On 2 June 2022 he scored against San Marino in UEFA Nations League D play in Tallinn.[40]