If 10 electors had requested an election (in writing), one would have had to take place not later than May 8.
It would have involved ballot papers being printed and polling stations organised, followed by a counting of votes cast.
However, no such request was made to the Returning Officer at North Lincolnshire Council.
So the vacancy will be filled by co-option at a future meeting of the Town Council.
There is a vacant seat following the resignation of Paul Keane.
When at full strength, Brigg Town Council has 19 members and holds monthly meetings in the Angel Suite, which are open to interested members of the public.
The next will be on Monday, March 27, starting at 7.15pm.
Brigg Town Council is based in the Angel building. Call 01652 659402 or email enquiries@briggmarkettown.co.uk
The co-option system is often used to fill vacancies on parish and town councils across the UK.
People interested in taking on the role make a written submission and if there's more than one applicant the current members of the council vote on which person they would like to see join the council.
PICTURED: The Angel Suite in use as a polling station on a past election day.