The Chieftain departed from runway 16R on a Radar 6 departure. After initial vectoring to avoid noise sensitive areas, the aircraft was vectored to intercept the planned track to Katoomba and instructed to climb to 5000 ft. The SAAB was cleared to Sydney via the Oakdale 2 arrival and had been cleared for descent to 6000 ft. The departures controller reported that he observed the Chieftain climb through 5000 ft, in close proximity to the SAAB. He immediately instructed the pilot of the Chieftain to descend to 5000 ft and vectored the aircraft away from the SAAB, as well as passing traffic information on that aircraft. The approach controller notified the pilot of the SAAB, regarding the Chieftain, and vectored the SAAB away from the other aircraft. Subsequent investigation revealed that the Chieftain had passed within 1.7 NM of the SAAB, with a vertical separation of 900 ft, resulting in a breakdown of separation. At the time of the occurrence the minimum required separation standard was either 3 NM laterally, or 1000 ft vertically.