This is completely missing from TNG, DS9, VOY and ENT.
Dennis McCarthy had a Picard motif that he used frequently throughout the first three seasons (perhaps most memorably in the climax of "Yesterday's Enterprise"), and Ron Jones had recurring motifs for the Klingons (based on Goldsmith's Klingon motif) and the Romulans, plus a recurring Enterprise
motif that he introduced once he decided the show had established its own identity and needed to move beyond the Courage fanfare and the Goldsmith TMP theme.
Listening to the TOS collection I'm struck by how we were deprived of a distinctive Romulan theme when Steiner reused (either by choice or not) many of his "Balance of Terror" motifs in "Mirror, Mirror" and Courage didn't use any of it in "The Enterprise Incident." It wasn't until Ron Jones came up with a great Romulan motif that stuck in TNG "The Neutral Zone" (but I'm not sure how many other TNG-era composers carried it over for their Romulan shows). And Steiner's great Klingon themes from "Elaan of Troyius" -- although IMHO an improvement over Fried's themes in "Friday's Child" -- probably came too late in the series run to make a lasting impression, so we got Goldsmith's long-lived Klingon theme in TMP that lasted for over 20 years (which Ron Jones -- to his credit -- revisited at least once ("The Defector") rather than coming up with something new.