The other option, as discussed by the five-member council on Monday, was to hold a special election.
Appointing the new council member will expedite the replacement process and save the city the estimated $30,000 a special election could cost, city officials said in a news release.
Molnar, who ran for mayor in November, resigned because she'll no longer be a full-time resident of Grover Beach, moving instead to a home in an unincorporated area of San Luis Obispo County.
The seat she held expires in December 2014.
Feb. 19 is the deadline for registered voters in Grover Beach to submit letters of interest for the seat to the city managers office at City Hall, 154 S. Eighth St. Letters must be submitted before the office closes at 5 p.m.
The council will interview candidates during a special City Council meeting scheduled for Feb. 25, according to the news release. The appointment must be made by April 1.
The council will be faced with making important decisions in the days and months to come, including decisions regarding the development of the next budget, how to maintain city services, improve economic development opportunities, complete the Grover Beach Lodge and Conference Center, and fix our streets, Mayor Debbie Peterson said in a statement.
Council members paid a stipend of $300 per month attend two council meetings per month and also serve on monthly subcommittees.
For more information on the application process, call City Manager Bob Perrault or City Clerk Donna McMahon at 473-4567.