Police enquiries are ongoing following a number of sectarian incidents at Grove Playing Fields in north Belfast over the past week.
he PSNI said they received a report that a woman who was walking in the park on Wednesday was subjected to verbal abuse by a group of men at around 4pm.
It's after a banner saying "Anti British GAA not welcome" was placed at the park's entrance last weekend. Graffiti with the same message was also sprayed on a wall in the grounds.
The message was later removed by Belfast City Council, who own the park. They said they're also aware of a separate incident on Thursday evening.
Local politicians have said a group of men gathered at Grove Playing Fields and told people wearing GAA and football tops to leave.
North Belfast MP John Finucane called for local political and community figures to show leadership over what he described as "attempts to mark out territory, intimidate residents and stoke up sectarian tension."
"Last weekend we had a banner erected at the Grove Playing fields attempting to intimidate members of the GAA from using a shared council facility.
"This was followed up by the intimidation of Catholic families and soccer players off the facility. This is a shared space owned by the council and which everyone should be able to use free from sectarian intimidation and harassment.
"Unfortunately these are not isolated incidents and there seems to be a concerted attempt going on to claim territory in clearly shared spaces, to intimidate residents and stoke up sectarian tensions in other areas of north Belfast.
"Cars were attacked last weekend, and residents are being abused as flags are erected in mixed areas of North Belfast.
"The police have a role in ensuring that residents remain safe in the face of sectarian harassment but there is also an onus on all community and political leaders to show leadership, to condemn these actions and do all in their power to bring them to an end."
A council spokesperson said: "Our parks are shared spaces for everyone to enjoy and we would encourage anyone who witnesses such incidents to report it immediately to the PSNI.
"It can also be reported to our anti-social behaviour officers on 9027 0469 or email firstname.lastname@example.org."
Speaking on Thursday, Belfast Deputy Lord Mayor Paul McCusker condemned the incident.
"This is a busy park and we have to do all we can to eradicate sectarianism that shouldn't be accepted anywhere and everyone should feel safe in all our parks," he said.
A north Belfast GAA member, who did not want to be identified, said the experience was "intimidating".
Speaking to BBC News NI, they said: "The fact that people have been chased off with their children, some as young as seven years of age, I mean no seven-year-old child, whether they're wearing a GAA top or a Northern Ireland top, they're no threat to anyone.
"This isn't even a club, it's parents and their kids getting fresh air and exercise.
"It's very damaging to the whole community, because in recent years there has been so much goodwill built up from all sides of the community.
"I don't think this is representative of the community."