The council is advertising after Coun Cara Sandy stepped down from her position on Castle Ward this month.
The public have until September 28 to request a by-election to fill the vacancy, sent in writing to the Returning Officer, Ian Fytche at North Kesteven District Council, Council Offices, Kesteven Street, Sleaford, Lincs, NG34 7EF.
There must be at least ten electors from Castle Ward calling for the vote.
If an election is called, it will take place no later than November 30.
If no request is made, the vacancy will be filled through co-option by the Town Council.