We fully support an HQ reference and there’s one in The Times’ cryptic today...

Let's break it down.
After some trial and error we can locate the straight part of this clue at the beginning — ‘dog’.
What dog can be made from the rest of the words? Well, the state of New Jersey can be referred to as ‘NJ’, and ‘one’ often indicates ‘a’ or ‘i’.
In this example it’s ‘i’. When ’NJI’ is attached to an army HQ, or ‘base’, we get a seven-letter dog breed: BASENJI.
basenji — a small smooth-haired breed of dog of African origin
If you were barking up the wrong tree with this one, we don’t blame you 😄