Divorce sergeant after break-up (8)

I believe the answer is:

estrange

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

'divorce' is the definition.
(I've seen this before)

'sergeant after break-up' is the wordplay.
'sergeant' can be anagrammed to 'ESTRANGE'.
Though, I am not sure how the anagram is indicated.

Can you help me to learn more?

(Other definitions for estrange that I've seen before include "Get on the wrong side of" , "Divorce" , "split up?" , "Ten gears (anag.)" , "As Regent (anag.)" .)

I've seen this clue in The Hindu.

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