Former UUP leader Mike Nesbitt, meanwhile, said he has no “difficulty” with PSNI seeking recruits through “sporting organisations” but said “balance” is important.
The PSNI advertisement, placed in the match programme for the match between Limerick and Cork on Sunday, isn’t the first time the police service has sought new recruits through the GAA.
It featured a smiling female officer and encouraged those who find that “keeping people safe” comes naturally to them to “déan slí bheatha de” – a Gaelic phrase which translates roughly to ‘make a living out of it’.
A similar full-page advertisement was placed in the match programme for the 2019 All-Ireland final.
The advertising campaign also marks a departure from previous GAA policy, who until 20 years ago banned members of “security forces” from taking part in the sports.
Mr Bryson, meanwhile, took to Twitter to ask “how many times have they advertised in Orange Order literature?”
Speaking to the News Letter, the loyalist figure said: “It seems the PSNI almost have hardwired into their DNA a perpetual need to appeal to the nationalist community, and there’s not an equal desire to try and appeal to and treat the unionist community with the same courtesy and the same type of approach.
“That’s the concern.”
Mr Nesbitt, meanwhile, told the News Letter he has no “difficulty” with the police service seeking new recruits through “sports associations” but said he would seek further information about PSNI advertising campaigns.
“I wouldn’t have a difficulty if they are advertising through sports associations,” he said.
“The question that it raises for me is where the PSNI is advertising for recruits, and as a member of the Policing Board I need to make myself more acquainted with where they are advertising to ensure that it is balanced.”
Pamela McCreedy, PSNI chief operating officer, said: “It is vitally important that any police service is representative of the entire community it serves.
“We have been and will continue to engage with all communities, particularly those who are under-represented within our organisation.”