Heritage council rules in Adelaide vary by council and by property. Here's the practical breakdown.
City of Adelaide
State Heritage Listed and contributory: roof material/colour changes require development consent via PlanSA. Like-for-like restoration usually exempt.
City of Burnside
Historic (Character) Areas covering Beaumont, Glenside, Kensington Gardens. Heritage Listed work needs consent.
City of Unley
Wide heritage character across Unley, Hyde Park, Malvern, Goodwood, Parkside. Heritage Listed work needs consent.
NPSP and Prospect
Similar inner-east heritage rules. Always check PlanSA listing for your specific property.