Kyle had been battling his sometime nemesis Grayven when he fell into a time-warp and wound up in the 30th Century, where he met the Legion of Super-Heroes.
The main thrust of the story deals with a much younger Hal having to come to grips with the new reality he's in; specifically, the fact that he's (at that time) one of the most reviled villains, and that his friend Ollie Queen is dead.
Hardy now intends to send a plane to Seattle with a bomb supplied by The Eden Corps, a group of radical environmentalists who were responsible for Ollie's death.
Acknowledging that he is proud to have him carry on the Green Lantern tradition, Hal hugged Kyle, whispering to him "You'll know what to do with it", before all three joined forces: Parallax would be responsible for returning everyone to their proper place in time, Hal's ring would wipe his and Parallax's minds of these events, and Kyle's ring acted to boost their power.
Kyle eventually copies Hal's power ring and gives it to Alan Scott's daughter, Jennifer-Lynn Hayden, allowing her to follow in her father's footsteps as the first female Green Lantern of Earth.
[1] In Green Lantern: The New Corps, during a weeks-long adventure in space, Rayner attempts to rebuild the Green Lantern Corps, recruiting Magaan Van'n Intraktus of the planet Van'n, Hammeroon (a bounty hunter from Ilskado System), Anya Savenlovich (a lieutenant colonel from Soviet Union Air Force who was in suspended animation after participating in a space mission in 1964), Garl Rathbone (a miner from the debris belt over the planet Daffith), and Sool (a judge, also from Daffith).
Kyle would later be possessed by Ion, the willpower entity, granting him the vast power he needed to create a new generation of Guardians.
After defeating and imprisoning Parallax, Ganthet and the reborn Guardians succeeded in rebuilding the Green Lantern Corps.