One's car could become rougher (7)

I believe the answer is:

coarsen

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

'one's car could become rougher' is the definition.
I can't tell whether this defines the answer.

'one's car could become' is the wordplay.
'could become' indicates an anagram.
'ones'+'car'='onescar'
'onescar' with letters rearranged gives 'COARSEN'.

Can you help me to learn more?

(Other definitions for coarsen that I've seen before include "become inferior" , "Dull" , "Make more harsh" , "Make rougher" , "Turn rough" .)

I've seen this clue in the Sydney Morning Herald.

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