Assistant Chief Constable Barbara Gray said it was too simplistic to attribute the recent spate of dissident attacks to Brexit.
But the officer, who heads up the Police Service of Northern Ireland's counter-terrorism response, warned it would likely become a motivating factor for extremists in the event of a disorderly exit.
As well as several recent attacks, one of which resulted in the murder of journalist Lyra McKee in April, Ms Gray revealed 10 other murder bids have been foiled in the last two years.
"We will be prepared and we will be very ready for any potential upsurge in violence that may happen after Brexit," she told the PA news agency.
"We predict that a six to 12-month period, if there's a no-deal Brexit, that there could be an upsurge in violence."
The PSNI is attempting to combat the threat from several dissident groupings.
The New IRA is the largest but a recent bomb blast in Co Fermanagh blamed on the Continuity IRA demonstrated the threat still posed by that group.
Officers also consider the smaller Arm na Poblachta (ANP) and Irish Republican Movement (IRM) as risks to national security.
"Anything that brings the border issue into question in Northern Ireland brings tension," Ms Gray said.
"I think in the last few weeks, probably since the new Cabinet, the new PM and his announcements (on the exit date) that 'this is October 31, this is what we're looking at', I think generally you can almost feel at bit of anxiety rising across society."
Ms Gray said policing the border in significant numbers to support any checks or controls that might be required in a no-deal scenario would bring risks for officers.
"If questions of the border are being brought into play that does bring with it pressures," she said.
"If we as a police service have to at times maybe support other enforcement agencies - could be agriculture or whatever else - that does bring us into the picture probably in a different style and tone than we have been policing around border areas for many years now.
"Overall, our assessment would be that we would be concerned for a six to 12-month time frame there would be some sort of upsurge in support for dissident republican groupings and activities."