Methuen is in the market for a new city solicitor after Peter McQuillan was denied reappointment to another two-year term by a City Council vote earlier this month. McQuillan has held the position since 2005. Applications were accepted until last Friday; now a group of finalists will be chosen by a search committee made up of five city councilors and two local attorneys. City Council chairman Sean Fountain said McQuillan will remain in his position until a replacement is hired, or until an interim solicitor is named. According to the job posting, contenders must be in good standing with the Massachusetts Board of Bar Overseers and have at least five years experience in municipal law.