Born in Skerries, Dublin, Oliver first began playing rugby for Skerries Under-8s, remaining with the club until his Leaving Cert year, when he joined Blackrock College and won the 2014 Leinster Schools Rugby Senior Cup alongside current Irish international Joey Carbery,[1] with Oliver scoring his sides opening try in their 22–17 win against Clongowes Wood College in the final.

[3] On 19 February 2016, Oliver made his competitive debut for Munster when he came on as a replacement for Tommy O'Donnell against Glasgow Warriors in a 2015–16 Pro12 fixture.

[8] On 31 March 2017, Oliver started for Munster A in their 2016–17 British and Irish Cup semi-final against Ealing Trailfinders, setting up Sammy Arnold's try and scoring two tries himself in the 25–9 win against the English Championship side at CIT.

[18] He made his return from the injury during Munster's Pro14 round 9 fixture against Italian side Zebre on 25 November 2018, replacing Chris Cloete during the second-half.

[19] Oliver joined Irish provincial side Connacht in July 2020,[20] and made his debut for the province in their 26–20 win against Ulster on 23 August 2020.