[1][2] An Alyawarra man, Reilly was born in Alpurrurulam on the Northern Territory/Queensland border and, in line with government policy of the day, was kidnapped from his mother and taken to Alice Springs hospital.
[7] Recruited by South Melbourne from Sunraysia Football League club Wentworth in 1962, Reilly made his senior VFL debut in Round Five that season against Fitzroy Football Club at South Melbourne's home ground, the Lake Oval.
[8] Over five seasons, Reilly played 51 games for South Melbourne, teaming with South's champion rover Bob Skilton to win matches "in an otherwise bleak period for the club",[9] with one sports reporter claiming "Elkin Reilly is not a brilliant player but his spoiling tactics are an important feature of South's play.
"[10] A ruptured appendix ended Reilly's VFL career in 1966 and he moved to Cohuna in country Victoria to coach.
[6] Rostrevor College has honoured Reilly by naming a hall and a scholarship for Indigenous students for him.