On 29 September 2013, Papalii played for Prime Minister's XIII, starting at second-row and scoring a try in the 50–10 win in Kokopo.

Papalii made his international debut for Australia against Fiji, starting at second-row and scoring a try in the 34–2 win at Langtree Park.

[21] Papalii played off the interchange bench in Australia's 34–2 World Cup Final victory over New Zealand at Old Trafford.

[24] On 12 June, Papalii was involved in a road rage incident after he threw a one-litre bottle of moisturising cream at another motorist, who subsequently insisted on a public apology.

The pair became involved in a heated exchange after Papalii allegedly cut off Mr Tutalo as he drove along Belconnen Way in Bruce.

Papalii played off the interchange bench and scored a try in the Kangaroos 22–18 Four Nations final loss over New Zealand at Westpac Stadium.

[29][30] In Round 22 against the Wests Tigers, Papalii played his 100th NRL game in the Raiders 20–18 loss at Canberra Stadium.

[41] Later on, 13 October 2016, Papalii withdrew himself from the squad due an ankle injury and was replaced by Manly-Warringah Sea Eagles player Jake Trbojevic.

[42] On 27 April 2017, Papalii was stood down by the Raiders for 1 match and the Kangaroos for the 2017 ANZAC Test after he was convicted of drink-driving after he bizarrely called triple 000 twice to report himself driving erratically in the early hours of 15 January 2017.

The court heard Papalii was sprung after police received an anonymous triple-0 call to report a black Jeep driving on the wrong side of the road in Gungahlin about 2.15am and police got a second call to say the same car had pulled over near Hungry Jacks about 20 minutes later, officers approached the vehicle on a bike path on Gundaroo Drive soon after and asked Papalii, who was in the driver's seat, to get out of the car.

Papalii had a blood-alcohol reading of 0.123 just hours after he left the engagement party of Raiders captain Jarrod Croker.

[49][50] In Round 1 against the Gold Coast Titans, Papalii played his 150th NRL career match in the 30–28 loss at Robina Stadium.

On 31 May 2018, Papalii spoke to the media about his shock axing to reserve grade saying "Our team wasn't going too well at the time and I knew someone had to go back.

[60] Papalii played at prop for Canberra in the 2019 NRL Grand Final as they were defeated 14–8 by the Sydney Roosters at ANZ Stadium.

Papalii had another outstanding season in 2020 for Canberra and was rewarded with his fourth Meninga Medal, this time sharing the award with Jack Wighton as they finished atop the voting for the club's player of the year.

[67][68] Papali'i played a total of 25 matches for Canberra in the 2022 NRL season as the club finished 8th on the table and qualified for the finals.

[70] Papali'i played a total of 18 matches for Canberra in the 2023 NRL season as the club finished 8th on the table and qualified for the finals.

[72][73] In the early hours of 16 September 2024, Papali'i and a friend were allegedly behaving aggressively, smashing glasses, and refusing to leave Canberra Raiders Leagues Club.