Both parties said then High Court Judge Douglas White erred in finding that a clause in a 2001 out-of-court settlement agreement applied to any accommodation on any part of Mr Kelly's property on Karikari Peninsula and not limited to land covered by the resource consents.
They said Justice White was also wrong in finding that the implementation of the land use consent was dependent on achieving a subdivision consent.
His findings that the decision by both sides not to notify Ngati Kahu was unreasonable despite the fact that provisions in the Resource Management Act excluded the need to do so, was also challenged in the Court of Appeal.
The council and Mr Kelly asked the Court of Appeal to quash the High Court judgment and to declare that the settlement agreement applied only to rented accommodation on that part of Carrington Farms, a company owned by the US billionaire.
The current court case had its origins in 2007 when the FNDC granted Carrington a non-notified consent to build 12 houses. It was only in 2009, when Carrington applied to subdivide the land, that Ngati Kahu learnt of the earlier consent.
The High Court ruled the applications should not have been allowed separately, and Ngati Kahu should have been informed on both occasions. That judgement is now being appealed.
Mr Kelly owns Carrington Club golf course, a luxury lodge and winery on 1200ha of land on Karikari Peninsula. He is a member of the New Zealand Business Roundtable.