In 1961, Norrish was posted to New York City as New Zealand's deputy permanent representative to the United Nations.

In 1972, he became acting high commissioner to London, before returning to Wellington as deputy secretary of Foreign Affairs in 1973.

During that period, Norrish was the key foreign policy official during New Zealand's withdrawal from ANZUS and the nuclear ship controversy.

[citation needed] During his tenure, French secret agents bombed the Greenpeace ship Rainbow Warrior in 1985.

[2] In the 2002 Queen's Birthday and Golden Jubilee Honours, Norrish was appointed a Companion of the New Zealand Order of Merit, for public services.