It follows the resignation last week of Tessa McLean who will be leaving to undertake a new career abroad.
Conservative councillor Tessa McLean won the seat for Old Gore, situated to the north east of Ross-on-Wye, at the local elections in May last year from Independent councillor and council chairman John Edwards, in what was her first election contest.
Anyone wanting to stand in the election should collect a nomination form from the council's Electoral Registration Office, in the County Offices, Bath Street, Hereford, HR1 2HQ.
The offices are open from 9am to 5pm Monday to Thursday, and from 9am to 4pm on Fridays (excluding Bank Holidays).
Completed nomination forms must be returned to the offices by midday on Wednesday, March 12.
Electors who want to vote by post must apply to the Electoral Registration Office by 5pm on Wednesday, March 26. Completed application forms must be returned by 5pm on Wednesday, April 2 - in exceptional circumstances (unforeseen illness or incapacity), applications may be made up until 5pm on the day of the election, April 10.
Anyone wanting more information about how to stand in the election or vote in the election can contact the electoral registration team on 01432 260107.