Prior to his tenure in the National Assembly, Stubbe was a Member of the Northern Cape Provincial Legislature.

On 10 September 2010, Stubbe was sworn in as a Member of the National Assembly, replacing Andrew Louw, who had been redeployed to the provincial legislature.

[4] DA parliamentary leader Athol Trollip appointed him as Shadow Minister for State Security.

[5] In February 2012, newly elected DA parliamentary leader Lindiwe Mazibuko named him Shadow Deputy Minister of Police.

[8] On 5 December 2020, Stubbe was appointed as Shadow Deputy Minister of State Security by John Steenhuisen.