*Club domestic league appearances and goals, correct as of 11 December 2024 (UTC) ‡ National team caps and goals, correct as of 19:53, 12 September 2023 (UTC)
On 9 July 2021, Osmajić signed a three-year deal with La Liga side Cádiz CF.[2] He made his top tier debut on 14 August, coming on in the 70th minute for Anthony Lozano in a 1–1 draw with Levante UD.
On 31 January 2022, Osmajić was loaned to Turkish side Bandırmaspor until June.[3] On 10 August, he switched teams and countries again after agreeing to a one-year loan deal with Portuguese Primeira Liga side F.C. Vizela.[4]
On 1 September 2023, Osmajić signed for EFL Championship club Preston North End on a four-year deal, for an undisclosed fee reported to be a club record for Preston.[5][6] His first goal came as the match-winner against Birmingham City on 19 September 2023 and allowed Preston to retain their spot at the top of the Championship.[7] On 9 April 2024, he came on as a late substitute in a home game against Huddersfield Town and scored a hat-trick in six minutes to cement a 4–1 win.[8] Without scoring a single goal in the period between the two, Osmajić scored another hat-trick for Preston in their 5-0 victory over Harrogate Town in the second round of the League Cup on 27 August 2024.[9]
On 22 September 2024, Osmajić caught attention following a derby match against Blackburn Rovers, as imagery suggested he had bitten opposition player Owen Beck’s neck; who received a red card, as he kicked-out at Duane Holmes. Osmajić received a yellow card, for dissent, during the incident.[10] He was subsequently banned by The FA for eight matches and fined £15,000.[11]