Having begun his career at FC Emmen in the Eerste Divisie, Dost later played in the Eredivisie for Heracles Almelo and SC Heerenveen.

Four years later, having helped his team win the DFB-Pokal he signed for Primeira Liga side Sporting CP.

He won the Bola de Prata for top scorer in his first Primeira Liga season, with 34 goals in 31 games.

[11] Dost started the 2014–15 season as Wolfsburg's third choice striker[8] and made his European debut[12] in a 4–2 win against FC Krasnodar in the Europa League.

Dost headed in the final goal from an Ivan Perišić cross as Wolfsburg won 3–1 over Borussia Dortmund at the Olympiastadion.

[18] He made his debut on 10 September at home to Moreirense F.C., concluding a 3–0 win;[19] thirteen days later he scored for the third successive game, netting twice in a 4–2 victory over G.D. Estoril Praia again at the Estádio José Alvalade.

[31] In April 2018, Dost ended a run of 45 first time finishes when he took a touch before scoring in a Sporting win against Belenenses.

[33][34][35] Despite the attack, he and the rest of the team agreed to play in the Portuguese Cup final scheduled for the following weekend,[36] losing 2–1 to Aves.

[39] On 25 May in the 2019 Taça de Portugal Final against the same opponents, he scored an extra-time goal and missed in the penalty shootout, but his team still won.

[41] He arrived to replace departed strikers Luka Jović and Sébastien Haller, on a fee reported as €7 million.

[43] Dost arrived at a club which had lost Jović, Haller and Ante Rebić in high-profile transfers, but combined well with Portuguese attacking duo André Silva and Gonçalo Paciência during his one full season.

[48] On 1 July 2022, FC Utrecht announced the signing of Dost on a one-year contract, as he returned to the Eredivisie after a decade abroad.

In August 2012, he was called up by new manager Louis van Gaal for a friendly match in the King Baudouin Stadium in Brussels against Belgium but did not feature.

[53] He made his debut in the first match on 28 March at the Amsterdam ArenA, replacing defensive midfielder Nigel de Jong after 63 minutes as the Netherlands equalised for a 1–1 draw.

[55] In April 2018 Dost announced his retirement from international football at the age of 28, saying that he had considered it for some time due to a lack of success with the national team.