A Cliftonville supporters group has called on the club to take action against striker Jay Donnelly
The 23-year-old Irish League footballer was sentenced on Thursday to four months in prison for distributing an indecent image of a child.
Cliftonville FC have said they were awaiting the end of the legal process.
The Irish Football Association has announced it is bringing in a new education policy for players in the wake of the sentencing.
North Belfast Reds supporters club has said Cliftonville's position is "unacceptable".
"The club must act swiftly and begin full disciplinary proceedings against the player," a statement said.
"To wait until the outcome of any possible appeal is unacceptable and damages the reputation of the club.
"Victims should be our prime concern, not those convicted."
Donnelly took a photograph of a 16-year-old girl while they were participating in a sexual act in June 2016.
He it to a friend and a WhatsApp group that included fellow Cliftonville players. The photograph was then leaked and appeared on Facebook.
Donnelly has been granted bail pending appeal.
Cliftonville FC said it would "not shirk responsibilities to members, supporters and the wider community".
In a statement the club said it did not condone the behaviour and "recognises the impact that this has had on the victim and her family".
"We condemn such actions without question," it continued.
"We understand and appreciate that our supporters and others would welcome detailed commentary and statements on this matter, but we are constrained by the framework within which we as employers are legally obliged to operate."
The Irish Football Association said Donnelly had been referred to the Irish FA's Disciplinary Committee which will decide if he has brought the game into disrepute.
"Following the case and the issues that it raised, the Irish FA in conjunction with the Northern Ireland Football League (NIFL) will introduce a new education programme around lifestyle, attitude and values for club players and staff. It is proposed that this programme will be linked to club licensing, making it mandatory," an IFA spokesperson said.