Sri Lanka have dropped skipper Dinesh Chandimal for their tour of South Africa and have named opener Dimuth Karunaratne as the stand-in skipper.
Chandimal said that while the team has been transitioning in recent years, and is still young, it was time for them to start performing.
Beating Sri Lanka 2-0 is Australia's first Test series win in over a year.
Starc picked up 4 wickets as Sri Lanka went to lunch at 87 for five, still 429 adrift on day four.
Sri Lanka's tour of Australia has been hampered by off-field setbacks and distractions.
Australia have named an unchanged playing XI for the second Test against Sri Lanka which gets underway from Friday.
When captain Dinesh Chandimal was asked about the murky situation, he said: "I don't have any comments on that."
Speaking to reporters ahead of Thursday's opening Test at the Gabba, Chandimal was cautious when asked about Sri Lanka's chances.
Sri Lanka are coming off a 0-1 defeat to New Zealand.
The conditions were tailor-made for short-ball specialist Wagner, New Zealand bowling coach Shane Jurgensen said, as Sri Lanka were 231 for six at stumps.