In 1903, it was initially reported that would contest the vacancy in the Legislative Council left by the death of Barrington Clarke Wood,[2] but he did not go on to nominate for the election.

On a then-record turnout of almost 8,000 voters, he polled 54.01 percent of the vote, replacing Harry Brown (who did not re-contest) as mayor.

[7] However, Stubbs re-entered the public arena the following year, when he was elected unopposed to the Legislative Council's Metropolitan-Suburban Province, replacing the retiring Zebina Lane.

Stubbs was nominated as the coalition's candidate for Speaker of the Legislative Assembly, and was duly elected to the post by parliament.

[15] Known for his habit of returning a full bow to members exiting the chamber,[16] Stubbs was praised by the opposition leader, Philip Collier, for his "impartial manner" in the position.

[17] One of his duties as speaker was to entertain visitors to Parliament House, and in that capacity he hosted the English cricket team, captained by Douglas Jardine, that toured Australia during the 1932–33 season – the Bodyline series.

[21] He consequently set a new record as Western Australia's oldest parliamentarian, which lasted only until September 1949, when it was broken by Sir Norbert Keenan.