Not much is known of Archon Z'gmora, he was ambushed in a temporal dimension by a creature named N'Gon. The creature had attempted to steal his power, for a battle with a duplicate of itself. Mortally wounded in battle, Archon Z'gmora destroyed his ring to keep it from his attacker. He called Hal Jordan for help.
According to Hal Jordan, Archon Z'gmora was friends with Norchavius and Zuron. Jordan wondered why Z'gmora had not requested help from them instead of him, as they hadn't been on friendly terms since an incident on Altair-Four.
Jordan had been lured into the same trap as Z'gmora. Fortunately, the Green Lantern of Earth split his body in two - one, his empty physical shell, the other, his spirit/astral form.
Seeking more power, N'Gon had planned to catch Superman in the same trap he'd used on the Green Lanterns. Jordan reintegrated his body, and with Superman's help defeated N'Gon. Presumably, Jordan later took Archon Z'gmora's body to Oa for entombment in the Crypts of the Green Lantern Corps.
[DC Comics Presents #26]
Archon Z'gmora is memorialized in the Crypts of the Green Lantern Corps on Oa.
[Green Lantern/Sinestro Corps: Secret Files #1]