Judge badly interrupting our time back in Peruvian city (8)

I believe the answer is:

trujillo

I'm a little stuck... Click here to teach me more about this clue!

'peruvian city' is the definition.
I know nothing about this answer so I can't tell whether this works.

'judge badly interrupting our time back' is the wordplay.
'judge' becomes 'J' (abbreviation for judge).
'badly' becomes 'i'll' ('ill' can be adverbial as in 'ill-advised').
'interrupting' is an insertion indicator.
'time' becomes 't' (abbreviation).
'back' is a reversal indicator.
'our'+'t'='ourt'
'ourt' in reverse letter order is 'truo'.
'j'+'ill'='jill'
'jill' going within 'truo' is 'TRUJILLO'.

'in' is the link.

Can you help me to learn more?

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.