Engelbrecht joined the
Democratic Party in 1991 and served as the party's branch chairperson at the Potchefstroom University from 1993 to 1995. In 2006, he was elected as a ward councillor in the
City of Tshwane Metropolitan Municipality for the
Democratic Alliance. He was selected as the DA's campaign manager for the City of Tshwane for the
2011 municipal elections. The DA caucus managed to grow 47 to 82 members and Engelbrecht was re-elected as a PR councillor at the election. He was then promoted to chief whip of the DA caucus. In
2014, he stood for the
Gauteng Provincial Legislature as 18th on the DA's list. The DA retained its position as the official opposition in the province and Engelbrecht was elected to the provincial legislature. During his first term, he was a member of the Governance & Administration Cluster Committees and the Infrastructure Development Committee. Engelbrecht was re-elected to the provincial legislature in
2019. He then became a member of the Roads and Transport Committee and an alternate member of the Economic Development, Environment, Agriculture & Rural Development committee. On 2 March 2021, Engelbrecht resigned from the Gauteng provincial legislature after the DA selected him to fill the late
Belinda Bozzoli's seat in the
National Assembly. He was sworn in as an MP on 4 March 2021. He was elected to a full term in the
2024 general election. ==Personal life==