Green's absence creates a headache in balancing the side and both the players called into the squad provide different routes.
Agar, who played the most recent of his four Tests in 2017, could bat at No. 7 and partner Nathan Lyon in a twin-spin attack should the SCG pitch, which has taken turn at various times this season, look dry for the Test.
He would likely have made the Test side in Sri Lanka earlier this year if he had not suffered a side strain during the limited-overs leg. His call-up now also puts him in prime position for a spot on the India tour in February where a left-arm fingerspinner is viewed as a key component.
"Ashton offers a second spin option should the Sydney pitch be conducive to turn, as it has done in the past," selector Tony Dodemaide said. "He also brings a solid batting component."
In the last two years Agar has only played three first-class matches which have brought seven wickets, largely due to being a regular in Australia's white-ball set-ups. He has been preferred ahead of legspinner Mitchell Swepson, who played in Pakistan and Sri Lanka, and the uncapped offspinner Todd Murphy.
If Australia opt for a more traditional balance then Renshaw, who has 11 caps and last played in 2018, could slot into the middle order. His versatility was noted by Dodemaide and would likely see him jump ahead of Marcus Harris who has been the spare batter in the squad throughout the Test summer.
"In terms of fast bowlers, it's a blessing to have Josh returning while Lance offers a genuine point of difference with his raw pace and skill," Dodemaide said.
Australia squad for Sydney Test vs South Africa Pat Cummins, Ashton Agar, Scott Boland, Alex Carey, Marcus Harris, Josh Hazlewood, Travis Head, Usman Khawaja, Marnus Labuschagne, Nathan Lyon, Lance Morris, Matthew Renshaw, Steven Smith, David Warner