In May 2021, Richard McCullough was chosen by Florida State University’s board of trustees to succeed Thrasher.

On November 17, 1998, Thrasher was unanimously elected as Speaker of the House for the 1999 through 2000 term, which passed legislation including "Three Strikes, You're Out", "10-20-Life", "A+ Education Plan", and the largest tax cut in Florida history.

[11] On September 15, 2009, Thrasher won the special Republican Primary election to succeed the late Senator Jim King.

[12][13] Thrasher defeated Ponte Vedra political activist Dan Quiggle, Jacksonville City Councilman Art Graham and former House Member Stan Jordan by garnering 39% or 13,247 votes in a four-way race.

[15] While in the Florida Senate, Thrasher served as the chairman of the Rules Committee and the vice-chair of the Budget Subcommittee on Higher Education Appropriations.

With the backing of his longtime ally, former governor Jeb Bush, he won easily his election to become the next chairman of the Republican Party of Florida and promised to improve transparency, communications and relationships with party activists, and to raise $1 million in six weeks.

In September 2014, Thrasher was appointed by the board of trustees of Florida State University by a vote of 11–2 to become the institution's 15th president.