This next batch of Leaguers were made up of characters that had a history with the JLA...and mostly had not been featured in strips of their own, unlike Green Arrow, Atom and Hawkman. Here's the facts behind the reprint collection cover by Jerry Ordway!
original Black Canary (Dinah Drake Lance) died after leaving Earth-2, and Superman took her to the Thunderbolt dimension, where here daughter was being kept safe (due to a spell by the JSA foe, the Wizard, cast on the child, young Dinah Laurel Lance) which gave her a wild uncontrollable sonic power. The Thunderbolt gave Dinah Laurel Lance her mother's memories, and Superman brought her to Earth-1 (where Dinah Laurel thought she was the original Black Canary; thus making Justice League of America #75 Dinah Laurel Lance's first appearance, and making stories like DC Special Series #10 of April, 1978, a daughter remembering her mother's origin...).
Hawkman as married police officers from the planet Thanagar, looking for fugitive shape-changer Byth, and stayed to learn Earth crime fighting techniques while using her flight, resistance to outer space, technological advances and ancient weapons to fight the new menaces they encountered!
Martian Manhunter in Adventure Comics #451 (probably both upset they never got to solo star with Batman in Brave and the Bold)...
Soon after this, Hawkman and Hawkgirl went back to Thanagar and got involved in the Rann-Thanagar War in Showcase #101-103 (June thru August, 1978), working with Adam Strange and Alanna against Kanjar Ro and Hyathis...and finding themselves exiled from Thanagar!
...unintentionally, to be replaced by the Hawkworld version of Hawkman and Hawkwoman, of which there is plenty to say on...later!
Mistress of Magic
Zatanna stuck it out for most of the team's move to the Motor City, but after the death of her father, Zatara, during the Crisis on Infinite Earths (chronicled in Swamp Thing #49 and #50 of June/July, 1986), and dealing with her mother's legacy in the Zatanna Special #1 (1987), she worked with the Spectre for a bit (himself dealing with a power down that happened during the Crisis on Infinite Earths)...