Moray MP Douglas Ross will be on the ballot paper for the contest after passing the 100-nomination threshold.
Carlaw steps down less than a year before the next Holyrood election.
The Scottish Conservatives accused Jeane Freeman of multiple failures and urged the FM to 'take the blinkers off'.
Jackson Carlaw has asked the FM to publish the evidence she is using as basis for adopting different stance from UK Government.
Scottish Conservatives call for more transparency on how funding is being allocated to local authorities.
Revealing his new shadow cabinet, new Scottish Tory leader Jackson Carlaw made a raft of changes.
The former finance secretary was forced to resign just hours ahead of delivering the budget on Thursday.
A debate on removing the EU flag from Holyrood after Brexit will take place on Wednesday.
Scottish Tory social security spokeswoman Michelle Ballantyne has joined the contest to become her party's next leader.
The SNP's Julie Ford accused Tory counterpart Mick Green in a series of tweets.