Lakes International Golf Management sent invoices to Vincent for $5070, representing three years of membership fees for the club.
The businessman, however, argued that because Lakes International was not an incorporated society it was not entitled to enforce the covenant.
A High Court judge ruled last year that Vincent owed Lakes International $5070 plus $602.84 worth of interest.
However, Vincent took the matter to the Court of Appeal and in August it found in his favour.
Justices Christine French, John Fogarty and David Collins of the appellate court said the definition of "golf club" in the covenant was clear and only permits one meaning.
"The obligations were imposed in relation to a golf club that was to be incorporated as an incorporated society to provide for playing rights on the golf course," the judges said.
The judges "were not without some sympathy" for Lakes International but said they could not justify "departing from the clear words of the covenant".
Lakes International, however, was this morning given leave to take the case to the Supreme Court.
While property owners in the Lakes Resort community have also resisted paying fees, they are not involved in the litigation. It is unclear how the final result will impact them.