Jarring was born on 12 October 1907 in Brunnby, Malmöhus County, Sweden, the son of Gottfrid Jönsson, a farmer, and his wife Betty (née Svensson).

[1] He served as director (utrikesråd) and head of the Political Department at the Ministry for Foreign Affairs in Stockholm from 1952 to 1956 and as an expert in the United Nations General Assembly in 1955.

[1] After several other diplomatic missions, he was Sweden's Permanent Representative to the United Nations from 1956 to 1958, and sat in the Security Council for the last two of those years.

After the 1967 Six-Day War and the adoption of UN Security Council Resolution 242, Jarring was appointed by the UN Secretary-General U Thant as a Special Representative of the Secretary-General for the Middle East peace process, the so-called Jarring Mission, during which he worked with the Four Powers who included United States UN Permanent Representative Ambassador Charles W. Yost.

[6][2] Gunnar Jarring continued to publish studies on Eastern Turkic languages throughout his diplomatic career and after retirement.