Growth on lip hurt after time (5)

I believe the answer is:

tache

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'growth on lip' is the definition.
'tache' can be an answer for 'growth' (short for moustache). I am not certain of the 'on lip' bit.

'hurt after time' is the wordplay.
'hurt' becomes 'ache' (synonyms).
'after' is a charade indicator (letters next to each other).
'time' becomes 't' (abbreviation).
'ache' after 't' is 'TACHE'.

Can you help me to learn more?

(Other definitions for tache that I've seen before include "show on one's face" , "Facial ornament" , "facial hair" , "Whiskers (informal)" , "Some bristles" .)

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