In 2010 and 2011, Cook played for the Penrith Panthers' NYC team. In 2012, he joined the Illawarra Cutters in the New South Wales Cup. On 30 October 2012, he signed a 1-year contract with the St. George Illawarra Dragons starting in 2013.
On 31 January and 1 February, Cook played for the Bulldogs in the 2015 NRL Auckland Nines. On 27 September, Cook was named on the interchange bench in the 2015 New South Wales Cup Team of the Year, for a second year. On 15 October, Cook signed a 2-year contract with the South Sydney Rabbitohs starting in 2016. Cook played a total of 37 reserve grade games for Canterbury and scored 2 tries.
2016
On 1 February Cook was named in the Rabbitohs' 2016 NRL Auckland Nines squad. On 6 March 2016 Cook made his debut for Souths against the Sydney Roosters and scored a try in Souths 42-10 win. Cook went on to play a further 17 times for the 2016 season. Cook also featured for Norths in The NSW Cup making 2 appearances.
Cook started the 2018 season as the first choice hooker for Souths over Robbie Farah. This year was Cook's most successful year.He made his debut for NSW in state of origin and the Australian Kangaroos. On 28 May 2018, Cook was selected to play for NSW against Queensland in the 2018 State of Origin series after a number of good performances at club level. Cook played in all 3 games for New South Wales as they won their first origin series since 2014. Cook was part of the Souths side which finished 3rd on the table at the end of the regular season and made it all the way to the preliminary final before being defeated by arch rivals the Sydney Roosters 12-4. He capped a stellar season by earning selection in the Australian Kangaroos team as starting hooker for Test matches against New Zealand and Tonga. On 5 December Cook signed a five year deal worth $4.5 million to stay with Souths until the end of 2023.
2019
After a good start to the 2019 NRL season for Souths, Cook was selected to play for New South Wales in the 2019 State of Origin series. In the series decider at ANZ Stadium, Cook scored a brilliant individual try as New South Wales defeated Queensland 26-20 winning their second series in a row. The match was won in the last 20 seconds courtesy of a try scored by James Tedesco. Cook made a total of 26 appearances for Souths in the 2019 NRL season as the club finished third on the table and qualified for the finals. Cook played in all three of the club's finals games as they reached the preliminary final against the Canberra Raiders. Cook had a game to forget in the preliminary final which culminated when he missed a one on one tackle with Canberra forward Josh Papalii who scored under the posts to win the match 16-10. On 7 October, Cook was named in the Australian side for the Oceania Cup fixtures.
2020
In round 10 of the 2020 NRL season, Cook scored two tries as Souths lost the match 20-18 against Newcastle at Bankwest Stadium.