He was arrested under section 41 of the Terrorism Act and taken to the serious crime custody suite at Musgrave PSNI station for questioning.
Gilmore died after he was shot in the Woodburn estate on Monday, March 13.
He was driving along Pinewood Avenue in his white Vauxhall Insignia car when a gunman opened fire on him, a bullet striking him on the neck.
Two men arrested yesterday have since been released without charge.
Detectives continue to appeal to anyone who was in the area at the time of the shooting and who witnessed the attack to contact them on the 101 number or on Crimestoppers on 0800 555 111.