A midfielder, 1.89 metres (6 ft 2 in) tall and weighing 87 kilograms (192 lb), Oliver is known for his capabilities on the inside due to his handball and clearance work.

[7] He was adjudged the best and fairest player in the TAC Cup by winning the Morrish Medal, where he received fourteen votes in the final nine rounds, and finished with fifteen in total, one vote ahead of Eastern Ranges forward, Darcy Crocker and Northern Knights midfielder, Jade Gresham,[9] in addition, he was named on the interchange in the TAC Cup team of the year.

[18][19][20] After the Melbourne Football Club unsuccessfully bid pick three in the 2015 national draft on Callum Mills, Oliver was recruited by them with their first selection and fourth overall.

[21] He was predicted by Fox Footy as one of the draftees who would have an immediate impact in the 2016 season,[22] and after playing well in the 2016 NAB Challenge,[23][24] he made his debut in the two-point win against Greater Western Sydney at the Melbourne Cricket Ground in Round 1.

[36] He played in the Victorian Football League (VFL) for Melbourne's affiliate team, the Casey Scorpions, the next week before returning to the senior side for the 73-point win against Gold Coast at Metricon Stadium in Round 7.

[46] During the off-season break after the 2016 season, Oliver failed a roadside random breath test whereby probationary (P-plate) drivers require zero blood alcohol content; he escaped club suspension, but he was fined an undisclosed amount.

[48] His drive during the pre-season drew public praise from his teammates including Aaron vandenBerg[49] and Tom McDonald,[50] and Melbourne's development and strategy coach, Brendan McCartney, who all stated they believed Oliver was the player to watch for the 2017 season, as he could take his "game to new heights.

"[51] Furthermore, former Melbourne captain Garry Lyon nominated Oliver as the player who could surpass all of his teammates in the future to become the club's best player by stating on SEN Breakfast: "they've got a great group of youngsters coming through ... and there's a boy called Clayton Oliver who I think is going to be better than all of them ... this guy is so good and clean in tight that I don't think most people—and I'm not putting him down—but unless you take a particular interest in the kid, you can't see how good he is.

"[52] Oliver played in the opening round of the season in the 38-point win against St Kilda at Etihad Stadium in which he recorded 36 disposals, fourteen contested possessions, eleven tackles and nine clearances, and was named "clearly the best player on the ground" by Fox Sports Australia journalist Anna Harrington[53] and AFL Media reporter Ben Guthrie.

[62] Furthermore, Melbourne's captain at the time, Nathan Jones, said Oliver was the best young talent he had seen in his eleven to twelve years of playing AFL football.

[65] Former Richmond player Matthew Richardson publicly defended Oliver amid claims he was a stager by saying: "Unless you're the one who's received that contact, how do you really know [how hard the hit was] ... he seems like a straight-up, honest kid".

[66] Schofield successfully appealed the original charge after arguing that while "he intended to strike Oliver and hit him with his forearm to the chin, the contact was so negligible it was not sufficient for a report".

[74] He was rewarded with the Keith 'Bluey' Truscott Trophy as Melbourne's best and fairest player when he polled 530 votes—184 ahead of Jack Viney, who placed second in the award—and received votes in every match for the season.