Gregory's car registration? Sydney's, actually (4)

I believe the answer is:

rego

'car registration? sydney's actually' is the definition.
(Australian term for a car registration)

'gregory's' is the wordplay.
'REGO' is hidden within the letters.
But, I'm unsure how the hidden word is indicated.

(Another definition for rego that I've seen is " Some overseas car owners cannot do without this".)

I've seen this clue in the Independent.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.