Numerous attempts to march have all been stopped by the PSNI.
Talks between Portadown District, the Garvaghy Road Residents' Coalition and Secretary of State Sir Chris Bryant have failed to find a solution to the prolonged stalemate.
The fresh Court of Appeal application argues that the Parades Commission had "materially misdirected itself" on the police assessment of the potential for disorder.
As members of the Garvaghy Road Residents' Coalition and their legal team entered the court building, there was applause and cheers from members of the crowd outside the court.
WATCH: Breandán Mac Cionnaith and Garvaghy Road Residents’ legal team greeted with applause and cheers as they arrive at court. pic.twitter.com/Khw019Pf1F