Alcott was a member of the Australia men's national wheelchair basketball team, known colloquially as the Australian "Rollers".

In 2014, he returned to wheelchair tennis with the aim of participating at the 2016 Rio Paralympics, at which he won gold medals in the Men's Quad Singles and Doubles.

Alcott continued to hold his spot and was a member of the Rollers when the team travelled to the Beijing Olympic warm-up tournament in January 2008.

[6] Alcott was part of the gold medal-winning Rollers team at the 2008 Summer Paralympics,[7][8] for which he received a Medal of the Order of Australia.

[12] In July 2014, he defeated world number three Andy Lapthorne 7–5, 6–1 in the British Open Wheelchair Tennis Championship final in Nottingham to win his first Super Series crown.

[13] In January 2015, he won the quad wheelchair Australian Open title by defeating David Wagner in straight sets.

[15] Alcott teamed up with Heath Davidson to win the Men's Quad Doubles gold medal at the 2016 Rio Paralympics.

[citation needed] He joined fellow professional wheelchair tennis player Diede de Groot in achieving the feat in 2021.

[19] Alcott has hosted Invictus Games Today, alongside Chris Bath and Anthony "Lehmo" Lehmann, and ABC's live music show The Set with Linda Marigliano.

[20] Alcott's return to wheelchair tennis after playing basketball resulted from an injury sustained in the lead-up to the 2012 Summer Paralympics.

[23] In 2018, he launched Ability Fest, a universally accessible music festival, featuring pathways for wheelchairs, quiet areas for people with sensory disabilities, and Auslan (Australian Sign Language) interpreters.

[26] Alcott's autobiography, Able: Gold Medals, Grand Slams and Smashing Glass Ceilings, written with help by Grantlee Kieza, was published by ABC Books in 2018.

[29] On 10 October 2023, Alcott was one of 25 Australians of the Year who signed an open letter supporting the Yes vote in the Indigenous Voice referendum, initiated by psychiatrist Patrick McGorry.