Agar was born in Melbourne, to a Sri Lankan mother and an Australian father, and has two younger brothers, Will and Wes. He attended Melbourne's De La Salle College, graduating in 2011.

He represented Victoria at both under-17 and under-19 level. After good form at the 2010–11 National Under-17 Championships, where he took 16 wickets at an average of 11.75 bowling left-arm orthodox spin, he was selected to play for the Australian under-19s for a series against the West Indies under-19s in the United Arab Emirates. Making his debut at the age of 17, Agar went on to play one under-19 Test and ten under-19 One Day International (ODI) matches for Australia. At the 2012 Under-19 World Cup, he was named in the squad as Australia's second spinner behind Ashton Turner, but did not play a match at the tournament.

Having failed to gain selection at senior level for Victoria, Agar moved to Western Australia for the 2012–13 season, where he was awarded a contract with the Western Australian Cricket Association (WACA). He made his first-class debut for Western Australia in a Sheffield Shield match against New South Wales in January 2013, replacing the injured Michael Beer as the side's spinner. In his second Shield match, early the following month, he scored 53 runs in Western Australia's second innings, putting on a state Sheffield Shield record partnership of 94 runs for the tenth wicket with Michael Hogan (43*). Agar made his List A debut for Western Australia in the limited-overs Ryobi One-Day Cup in late January, and took five wickets from his two matches, with his best figures 3/51 against Queensland.

Agar made his Sheffield Shield debut in January 2013. The following month, he was called up for Australia's 2012–13 tour of India, where he played a single tour match. Agar toured England and Ireland with Australia A in mid-2013, performing well in the English conditions. Although originally not selected in the touring squad, he made his Test debut for Australia in the first Test of the 2013 Ashes series. Coming in with the score on 117/9, Agar scored 98 runs batting eleventh in Australia's first innings, Agar broke several Test records on debut, including the highest score by a number-11 batsman and the highest partnership for the tenth wicket (with Phillip Hughes – since broken). However, after poor bowling, he was dropped from the team after the second Test of the series.

In February 2013, Agar was a late inclusion in the Australian squad for the 2012–13 tour of India, and played a single match on tour, taking 3/107 against India A. He finished the Sheffield Shield season with 19 wickets from five matches, including a five-wicket haul, 5/65, taken against South Australia in early March. In the same match, Agar was again involved in a sub