Abbott made his List A debut for New South Wales against Western Australia at the Sydney Cricket Ground on 17 October 2010 in the 2010–11 Ryobi One-Day Cup, but neither bowled nor batted in the match.

[4] During a Sheffield Shield match on 25 November 2014, Abbott bowled a bouncer that hit Phillip Hughes on the neck.

Hughes died two days later at St Vincent's Hospital, Sydney, as a result of a vertebral artery dissection, leading to subarachnoid haemorrhage.

[13] In November 2020, in round four of the 2020–21 Sheffield Shield season, Abbott scored his maiden century in first-class cricket.

He was awarded the Bradman Young Cricketer of the Year at the Allan Border Medal ceremony by the CA in 2015.

[21] In 2019, Abbott made his return to Australia's international side after a five-year hiatus, taking 2/14 off his four overs against Pakistan at Optus Stadium.

[22] On 16 July 2020, Abbott was named in a 26-man preliminary squad of players to begin training ahead of a possible tour to England following the COVID-19 pandemic.

[23][24] On 14 August 2020, Cricket Australia confirmed that the fixtures would be taking place, with Abbott included in the touring party.