He played and debuted as a fullback earlier in his career with enormous success and has represented Queensland in that position but settled into five-eighth upon Billy Slater's return from injury in 2017.

[14] From Round 12 onwards after incumbent fullback Billy Slater was ruled out for the rest of the year due to a shoulder injury, Munster stepped up and filled in the vacant position at ease.

[20] On 31 January, while in the Emerging Maroons camp, he broke curfew and the QRL announced he would be excluded from its representative programs for the next 12 months.

[22] Munster started the 2016 season playing at centre in round 1 against the St George Illawarra Dragons in the 18–16 win at AAMI Park.

[25] On 2 October 2016, in the Storm's 2016 NRL Grand Final against the Cronulla-Sutherland Sharks, Munster played at fullback in the 14–12 defeat.

However, with coach Craig Bellamy opted to rest Billy Slater for the opening 2 rounds of the season, Munster filled-in again at fullback with Ryley Jacks playing five-eighth.

[27] When fullback Billy Slater made his return from injury (coming off the bench in the 28th minute) in the Storm's Round 3 home game against the Brisbane Broncos, Munster then took over the five-eighth role.

[30][31] On-debut, he produced an outstanding performance combining with his Storm team-mates in QLD's one-club spine combination of Cameron Smith at Hooker, Cooper Cronk at Halfback and Billy Slater at Fullback; to help QLD to a series win in the 22–6 victory over NSW at Suncorp Stadium.

[32] On 1 October 2017, in the Storm's 2017 NRL Grand Final against the North Queensland Cowboys, Munster played at five-eighth in the 34–6 victory.

[33][34] Munster finished off a great 2017 NRL season with him playing in 21 matches, scoring 1 try and kicking 12 goals for the Storm.

[35][36] On 3 November 2017, Munster made his test debut for Australia against France, where he started at halfback in place for James Maloney who pulled out of the match the night beforehand for personal reasons and scored 2 tries in the 52–6 win at Canberra Stadium.

Munster's second sin binning in the game came after he kicked Sydney Roosters player Joseph Manu in the back of the head.

During game one, Munster was placed on report after kicking New South Wales player Liam Martin as he attempted to play the ball.

[43] Munster played a total of 21 games for Melbourne in the 2021 NRL season as the club won 19 matches in a row and claimed the Minor Premiership.

[48] On 8 July 2022, less than a week out of the Origin decider, breaking news began circulating that both Munster and QLD winger Murray Taulagi had returned positive Rapid Antigen Tests for COVID-19.

[50] In round 21 of the 2022 NRL season, Munster, starting a game at fullback for the first time since the 2019 State of Origin series decider scored the second hat-trick of his career in Melbourne's victory over the bottom placed Gold Coast Titans.

[51] Following great speculation with the new 2023 Redcliffe Dolphins and uniting with Wayne Bennett, Munster pronounced his loyalty to Craig Bellamy and Melbourne Storm by inking a new long-term contract.

[57] Munster played a total of 17 games for Melbourne in the 2024 NRL season as the club were runaway minor premiers.