Cabinteely have decided to drop their appeal to the Court of Arbitration for Sport (CAS) relating to the FAI and Wexford FC.
The Dublin club had taken issue with the eligibility of a Wexford player during last season.
In mid-October, the FAI found Wexford in breach of fielding an ineligible player in four matches, including an August fixture against Cabinteely.
What had played out as a 0-0 draw was awarded as a 3-0 win to the Stradbrook side.
However, a fortnight later an Independent Arbitrator who found in favour of Wexford regarding the fielding of Ola Adeyemo. Wexford had put the matter down to a clerical mistake on behalf of the FAI.
That meant Cabinteely lost their First Division playoff spot to Galway United.
The outstanding appeal to CAS had left the very make-up of this season's First Division up in the air, but positive talks with new FAI CEO Jonathan Hill have seen the matter resolved.
"We welcomed the opportunity to discuss this case with the FAI CEO and we thank him for his understanding of where we sit on this issue as a club," said Cabinteely chairman Larry Bass.
"Our approach to all of this was about fair play and the requirement for rules to be adhered to and not open to interpretation. The appeal was not lodged for monetary gain nor did we ever expect that the fixture in question or any part of the 2020 season could be replayed.
"Jonathan has accepted our reasoning for taking this case to CAS and he has agreed that the FAI will work with all the clubs to review processes accordingly.
"With that agreement in place, we are happy at Cabinteely Football Club to withdraw our appeal to CAS and we now look forward to the new season ahead."
Hill added, "On behalf of the Association, I want to thank Larry and his colleagues at Cabinteely for their approach to this difficult situation for all concerned.
"We acknowledge that the initial mistake over the player’s registration, which was outside of the control of the FAI, led to this dispute.
"Whilst that mistake was not of our making, there are clearly lessons to be learned and we will work closely with all our clubs now on the registration of players to ensure that such an issue should not arise again.
"I am delighted that we can all move on now and wish everyone at Cabinteely FC the very best ahead of the new First Division season.”