The 17th Amendment, ratified in 1913, allows for governors to fill a vacant Senate seat with an appointment until the next general election, or in some states, a special election.
In the last 50 years, 32 appointed senators have sought re-election. Of those 32, six (roughly 19%) were defeated in the primary, seven (roughly 22%) were defeated in the general election, and 19 (roughly 59%) were re-elected. Meanwhile, the re-election rate for all senators was 84% in 2018, in line with the average of about 83% over the last 50 years.