CALNE town councillor Mark Tong has resigned leaving a vacancy in the Abberd ward.
Mr Tong, who has held the seat for just eight months, is moving to Lincoln.
Deputy town clerk Linda Wakefield said the council would not be co-opting a new member.
"We will have a by-election provided we get the support for one," she said.
To hold a by-election ten electors from the ward must request a by-election in writing to North Wiltshire District Council.
The town council has put up notices informing electors of Coun Tong's resignation.
The request for a by-election must be submitted by January 29. Those wishing to stand for the town council will need to have a proposer and seconder.
The town council is responsible for allotments, by-laws, bus shelters, cemeteries, footpaths, sports and leisure facilities and parks.
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