The PSNI must be given extra resources to help them prepare for the dangers of terrorism that could come after the UK leaves the EU in March.
DUP deputy leader Nigel Dodds has raised the issue with the Prime Minister, while the Alliance Party's Stephen Farry has also called for additional resources for the police as they plan for problems, including protecting any border checkpoints from terrorist attacks and the possibility of a rise in cross border smuggling.
It comes after Northern Ireland's top police officer accused the Government of failing to understand the impact of Brexit and the dangers of terrorism in the region.
PSNI Chief Constable George Hamilton warned that government officials have failed to prepare for the impact of Britain leaving the European Union on issues surrounding peace and security.
He said that he has made a number of "urgent pleas" for resources, but he is not getting the information or clarity from Westminster he needs.
He also said that some politicians believed that terrorism in Northern Ireland was over and that it viewed the region as "peripheral".
"There's a feeling that as regards the Troubles and the conflict, Northern Ireland is sorted and we don't need to worry about it, when actually we're working flat out 24/7 to keep a lid on it," he said.
His comments have prompted a group that represents Northern Ireland students to issue a call for the government to speak with young people in Northern Ireland to garner their views on the impact of Brexit.
Doire Finn from Our Future Our Choice said: "I think that the points raised by Mr Hamilton were very important.
"Our Future Our Choice are a group of young people from Northern Ireland who have grown up without the threat of the Troubles, and Brexit seeks to drag us back into a dark past.
"So many of us live very close to the border and the fact that the Government isn't seeing the severity of the situation is very worrying.
"I would urge the Government to speak to young people such as ourselves and ensure that they understand the implications of Brexit on Northern Ireland.
"We deserve the right to be involved in a conversation which is going to massively impact on each and every person living in Northern Ireland."
With just six months until the Brexit deadline, Mr Hamilton made headlines yesterday with a hard-hitting interview in The Sunday Times, in which he said that any physical infrastructure would become a target for dissident republicans.
He said that the PSNI has been pressing the Government for more resources to prepare for Brexit.
When asked if the Government understood the full consequences on Northern Ireland, he said: "I'm not sure all of them do. I have a concern some may see issues to do with the Irish border as literally peripheral, not just geographically but in terms of impact."
He also criticised the lack of political stability in Northern Ireland after the Executive collapsed 20 months ago.
He said: "That's not a good thing.
"We would much prefer the government to be up and running, delivering on a programme and making people feel the benefits of peace and normality instead of this tension and nervousness."