Ms Hamilton was elected as a list MSP for the South of Scotland in 2016, but hopes to win the constituency seat vacated by Tory colleague John Lamont.
The Ettrick, Roxburgh and Berwickshire by-election will be held on 8 June, the same day as the snap general election.
Ms Hamilton's list seat remains with the Conservatives, with Michelle Ballantyne next on the list.
She leads the Conservative group on Borders Council, so a decision on whether she takes up the Holyrood seat will not be taken until after Thursday's council elections.
The Ettrick, Roxburgh and Berwickshire by-election was triggered by the resignation of Mr Lamont, who is contesting the corresponding Berwickshire, Roxburgh and Selkirk constituency in the Westminster election.
He is seeking to unseat the SNP's Calum Kerr, who has the slimmest majority in Scotland of 328 votes or 0.6% from the 2015 vote. Also contesting that election are former Labour MP Ian Davidson and Lib Dem Caroline Burgess.
Meanwhile in the Holyrood seat, which Mr Lamont held with a majority of 23.4% in 2016, Labour have put forward Sally Prentice and the Lib Dems are standing Catriona Bhatia.
Conservative MSP Rachael Hamilton has resigned from her seat to stand in a Holyrood by-election.