Councillors Kevin Hyland and Mary Duniam will move motions to increase the pressure on Cr Darren Fairbrother, who told The Advocate earlier this month that he intended to stay on as councillor.

Cr Hyland's motion will ask the council to move a vote of no confidence in Cr Fairbrother.

"Councillors, council staff and the community need this nation-wide embarrassment to end," Cr Hyland said in background material included in the agenda.

An officer's comment in the agenda says regardless of whether this motion gets adopted by the council, it will not result in any legislative outcomes as there is no provisions under the Local Government Act that covers a vote of no confidence.

While Cr Duniam's motion doesn't specifically mention Cr Fairbrother, she does mention his sentencing in background material supporting the motion.

Cr Duniam is calling on the council to write to the state government requesting them review the eligibility criteria for potential candidates to nominate for and/or hold the office of local government councillor in Tasmania.

She hopes this review will result in nominees and elected members undergoing a mandatory police check, a requirement that they provide a criminal history and they must have a current Working with Vulnerable People registration.

Cr Duniam will also call for a stronger code of conduct process to ensure fairness and equity for all code of conduct participants and reduce ethics and compliance risks and also changes to the Local Government Act that will mean councils could suspend or stand down councillors.

Following Cr Fairbrother's decision to not resign because "the summary offence that I have been charged for doesn't force me to resign", the state government revealed they were considering medium-term changes to the Local Government Act.

Ahead of the two motions, Cr Fairbrother has asked for data to be provided on how many motions and questions, with or without notice, each councillor has put forward during the current term and how many meetings and workshops each has attended.

Looking at the data provided in the council agenda, it shows Cr Fairbrother has been prolific in his involvement in council meetings.

His question follows a question from a member of the public late last year about how councillors were intending on best serving the community between then and the upcoming October elections.