Parker, the chairman of the House Republican Caucus, joins state Reps. Phil King of Weatherford and John Zerwas of Richmond in vying for the gavel. King declared his candidacy before Straus announced in October that he was retiring, while Zerwas got in quickly after Straus' announcement.
Announcing his speaker campaign, Parker said he was resigning as caucus chairman to focus on the race.
"I am ready to continue to serve Texas in a new leadership role bringing a unified effort for the betterment of our members and this great state," Parker said in a statement. "Yet, we have much more work ahead, and I am prepared to lead. Together, we will keep Texas the leading state for prosperity, liberty and opportunity."
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First elected in 2006, Parker represents House District 63 in North Texas. In addition to the GOP caucus, Parker chairs the House Committee on Investments and Financial Services.
Parker's entrance into the speaker's race comes two days after the primaries. Parker was unopposed for his House seat Tuesday, though he faces Democrat Laura Haines in November.
Straus is stepping down after a record-tying five terms as speaker. The race to replace him behind the gavel is expected to draw at least several more candidates.
Ahead of the 2019 session, House Republicans have agreed to select a speaker in the caucus and then vote as a bloc on the floor — a move that would make Democrats irrelevant in picking the chamber’s next leader. Before the primaries, the Texas GOP pushed House incumbents and candidates to sign a form promising to ultimately support the caucus pick — Parker and King have signed the form, while Zerwas has not.