He is the younger brother of fellow rower Valent Sinković, with whom he has won three Olympic gold medals.

[9] Sinković first took part in the European championships in their fourth iteration, held in 2010, with his brother Valent, David Šain and Damir Martin in the quadruple sculls category.

[13] The two brothers continued competing in the coxless pair in the 2019 European Rowing Championships as well, holding the leading position throughout the race, and finishing first with a time of 6:22.46.

[15] Together with Šain, Martin and his brother, Sinković participated in the 2012 Summer Olympics in London, in the quadruple sculls event.

[16] Sinković would change disciplines for the 2016 Summer Olympics in Rio, competing in the double sculls event, together with his brother.

In the final race of the event, the brothers held a narrow lead over the Lithuanian representatives, who overtook them by the 1500 meter mark.

[19] Sinković competed in the 2020 Summer Olympics in Tokyo, entering the coxless pair event with his brother Valent.

The pair entered the final race as overwhelming favorites to win the gold medal, with a betting coefficient of 1,03 and won with a time of 6:15.29.

[24] The same team competed in the 2013 World Rowing Championships, in the same category, finishing with a time of 5:53.57 and winning the gold medal.

[30] Martin and Valent Sinković took part in the 2022 World Rowing Championships as well, competing in the double sculls event.