During February and March 1963, "Anzac" served as escort for Queen Elizabeth II and the Royal Yacht "Britannia" during the royal tour of Australia. In October, "Anzac" accompanied the troop transport on a training cruise in northern Queensland waters. During May and June 1964, the destroyer embarked the Governor-General, Viscount De L'Isle for a visit to the territories of Papua and New Guinea. In September 1965, "Anzac" and the carrier escorted "Sydney" on the outbound leg of her second troop-transport voyage to Vietnam. On 21 May 1968, "Anzac" and "Sydney" left Brisbane on the latter's eleventh of twenty-five Vietnam voyages. The ships arrived at Vũng Tàu on 1 June, and returned to Brisbane on 13 June. During 1969, "Anzac" visited Tahiti and Western Samoa, and was in New Zealand for the bicentenary of James Cook's landing at Poverty Bay. In 1970, the destroyer was part of another bicentenary celebration of Cook's first voyage of discovery; this time at Cook's last Australian landfall at Possession Island. During the training cruises of the ship's final years, "Anzac" visited Papua New Guinea, Fiji, and New Zealand.