Governors cannot appoint replacements to House seats. Depending on the state’s laws they can choose not to hold the special election to fill the seat.
Hochul has 10 days to call a special election.
https://www.politico.com/news/2023/12/01/santos-expelled-special-election-00129590
Thank you, I didn't know that.
From the Congressional Institute:
For a vacancy in the House, Article I, section 2, provides that the chief executive of each state is to call for an election to fill the vacancy. For the Senate, the Seventeenth Amendment, which provided for the popular election of Senators, specifies that the executive should call for an election, and it also allows the state’s legislature to authorize the governor to make a temporary appointment until the special election is held.