VH-EAA was processed into the Sydney Terminal Area by the Approach south radar control sector, and was tracking via the 094 VOR radial, on descent to 6,000 ft in visual conditions. At 9 DME, the flight crew, in response to a TCAS RA alert, climbed the aircraft approximately 300 ft. They did not advise ATC of the alert. VH-NEK had departed runway 16L, on initial climb to 5,000 ft, and was being processed to depart the Sydney Terminal Area by the Departures south radar control sector. The aircraft was vectored onto a north-easterly track from a left turn after takeoff. Recorded radar information indicated that VH-EAA had continued descent to a pressure altitude of 5,700 ft and VH-NEK had climbed to a pressure altitude of 4,900 ft. When their flight paths crossed, VH-EAA was 800 ft above, and 1.86 NM to the right of VH-NEK. The traffic management plan, techniques and procedures, for processing both aircraft were adequate to maintain prescribed separation standards and tolerances in accordance with the runway 16 airspace agreement. However, neither controller had recognised the incident, probably due to the short duration of the encounter, and the lack of advice from either flight crew. Findings 1. The traffic management procedures adopted by the controllers for processing the aircraft were adequate. 2. VH-EAA descended below the assigned altitude. 3. In response to the TCAS RA alert, the flight crew returned the aircraft to the assigned altitude. Significant factors 1. The required separation standard was infringed when the flight crew permitted VH-EAA to descend below their assigned altitude.