Rank-and-file gardai want to wear a beard while on duty.
A motion due to be discussed at this week's Garda Representative Association (GRA) is calling for a change to the Garda Code to allow officers to sport beards while on duty.
Current rules state that officers must be clean-shaven around the jaw line and moustaches should be tidy and trimmed.
The GRA represents 10,300 members who are represented by 152 delegates from each of the 31 Garda divisions at the conference, which starts today.
GRA president Ciaran O'Neill will address Garda Commissioner Noirin O'Sullivan and Justice Minister Frances Fitzgerald tomorrow, six months after an unprecedented garda strike was averted.
A large number of motions will be debated by the delegates, including calls for better training, such as firearms instruction for officers, the provision of more "suitable and functional" garda uniforms and better working conditions.
The controversial watchdog, the Garda Siochana Ombudsman, is also expected to be criticised by gardai at the event.
However, the motion by gardai based in Kildare for the right for officers to grow beards is one of the more unusual discussion points.
The issue has been the focus of debate in the past when, almost 16 years ago, retired Garda whistleblower John Wilson fought and lost a campaign for gardai to be allowed to grow beards in 2001.
The GRA backed Mr Wilson's campaign in 2001 as well.
Mr Wilson suffered from an unusual skin condition, which was eased by growing a beard.
But, because this breached regulations, he was confined to indoor duties at Monaghan Garda Station.
He was advised to stop shaving by a garda doctor.
Despite a garda medical officer backing up this opinion, as a uniformed officer, he was still ordered to shave.
Mr Wilson turned down an offer of a plain-clothes position and claimed that he would have suffered financially if he had taken the job.