Admiral Leslie was a Federation Starfleet flag officer on active duty in at least the mid-23rd century.
In the 2260s, Admiral Leslie was assigned to the Starfleet Operations division. He had at least one son, also serving in Starfleet. (Star Trek: New Voyages: "Come What May")
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In an alternate continuity, his given name was Edward and he was chief engineer of the SS Yorktown in the late 2220s.