Admiral Parker was a male Vulcan Starfleet command division flag officer involved with Starfleet Academy enlistments during the 2370s.
In 2381, Parker attended the Command Conference on Starbase 25 where Ensign Brad Boimler, posing as William Boimler, spied him at the afterparty held in Ballroom Alpha. (LD: "An Embarrassment Of Dooplers")
Parker's name was among those reviewed by Sam Rutherford on a PADD titled "enlistment history". As he reviewed the roster in 2381 during his initial attempt to recognize who it was that attempted to blow him up, and based on his best guess, he figured it "must have been a higher-up in Starfleet back when I was a first-year, but that doesn't really narrow it down. It could have been anybody." (LD: "Reflections")
Much later that year, he was at Starfleet Command where he attended Captain Carol Freeman's questioning on the failure of Project Swing By. (LD: "The Stars At Night")
Parker was identified by name via the image that appeared on Rutherford's PADD in "Reflections".