Australian Capital Territory (Self-Government) Act 1988

At the first meeting of the Assembly after a general election, the members present shall, after electing a Presiding Officer and before any other business, elect one of their number to be the Chief Minister for the Territory.

If there is a vacancy in the office of Chief Minister (not because of a dissolution of the Assembly), then:

if the vacancy happens at a meeting, the members present shall elect one of their number to be the Chief Minister; or

if the vacancy happens at any other time, the Presiding Officer shall, by notice published in the Territory Gazette, convene a meeting as soon as practicable and, at the meeting, the members present shall elect one of their number to be the Chief Minister.

If a resolution of no confidence in the Chief Minister is passed, the members present shall elect one of their number to be the Chief Minister.