Heremaia has signed a contract with Widnes Vikings for the 2015 campaign after being told he would not be offered a new deal once his current contract expires at the end of this season.
The 31-year-old hooker will now see his three-year spell at the Black and Whites brought to an end after Hull opted to go in a different direction.
With Danny Houghton already signed to a long-term deal, Hull are keen to see Cunningham provide him with competition next year, having impressed during a season-long loan spell at London Broncos this time around.
Cunningham has not played a Super League game for Hull since making his breakthrough against Catalan in 2012, but FC are keen to give the 20-year-old home-grown talent an opportunity to shine.
Held in high regard at Hull, it is the emergence of Cunningham which has persuaded coach Lee Radford to let Heremaia leave.
Motu Tony, Hull's Football Manager, said: "We need to find a better balance in the squad, both across a number of positions and in terms of our salary cap, and giving our young players the chance to develop helps us do that.
"We have seen the emergence of a number of academy graduates in the first-team over the last 18 months and James Cunningham will be given every opportunity to do the same.
"Danny Houghton and James can develop a strong partnership in that role from next season, which means we can utilise a good amount of salary cap to secure the additions of some big signings we're looking to get completed for 2015.
"Aaron has given us great service over the last couple of years, but we must now focus on other areas of priority for the team. There are areas of our team that need significant improvement and this gives us the opportunity to do that and make a purposeful move for the targets we have identified and want to bring to the club."
Heremaia had initially been expected to retire at the end of this season, but had a change of heart at the beginning of the year after insisting he wanted to now play on for as long as possible.
The Kiwi is understood to have preferred to extend his contract at Hull, where he has settled and even joined the under-19s coaching staff.
However, Radford will now utilise the money to strengthen his squad elsewhere.
While Heremaia is not one of Hull's highest earners, Radford is eager to go with a slimmed down squad next season. He sees no sense in carrying three hookers and will use the money elsewhere to re-mould his side.
