[10][11] On 30 September 2012, in the Bulldogs 2012 NRL Grand Final against the Melbourne Storm, Finucane played off the interchange bench in the 14-4 defeat.

In round 20 against the Parramatta Eels, Finucane scored his first NRL career try in Canterbury-Bankstown's 40-12 win at ANZ Stadium.

[17] On 5 October 2014, in Canterbury's 2014 NRL Grand Final against the South Sydney Rabbitohs, Finucane played off the interchange bench in the 32-6 defeat.

[20] In round 1 of the 2015 NRL season, Finucane made his club debut for the Melbourne Storm against the St. George Illawarra Dragons, starting at lock in the 12-4 win at Jubilee Oval.

[30][31] Finucane finished the 2017 NRL season on a high with him playing in 26 matches, scoring four tries and kicking one goal for the Melbourne club.

However a late change by coach Brad Fitler saw Finucane start the match at lock in place of Paul Vaughan who dropped to the bench and Jake Trbojevic came into the front row.

At club level, Finucane played 26 games as Melbourne won the minor premiership and were amongst the favourites to take out the title.

On 19 February, Finucane and Jesse Bromwich are announced as co-captains of Melbourne, succeeding Cameron Smith.

[36] Finucane played 17 games for Melbourne in the 2021 NRL season as the club won 19 matches in a row and claimed the Minor Premiership.

[37] In round 1 of the 2022 NRL season, Finucane made his club debut for Cronulla-Sutherland in their 24-19 loss against the Canberra Raiders.

[39] On 26 July, Finucane was suspended for two matches after using a dangerous high tackle during Cronulla's round 19 loss to the Penrith Panthers.

[42] In round 3 of the 2024 NRL season, Finucane was taken from the field during Cronulla's upset loss to the Wests Tigers.

[43] On 23 April 2024, Finucane announced his immediate retirement from rugby league on medical advice, due to repeated head knocks.