Mounting rush to enter fashion in the clothing industry (3,5)
I believe the answer is:
rag trade
'the clothing industry' is the definition.
(I've seen this before)
'mounting rush to enter fashion' is the wordplay.
'mounting' says the letters should be written in reverse (in a down clue, letters mount or go up).
'rush' becomes 'dart' (both can mean to move quickly).
'to enter' means one lot of letters goes inside another.
'fashion' becomes 'rage' (something all the rage is fashionable).
'dart' written backwards gives 'trad'.
'trad' put inside 'rage' is 'RAG TRADE'.
'in' acts as a link.
(Other definitions for rag trade that I've seen before include "dressmaking competition" , "Informally, the clothing business" , "National winner" , "newsagent's business?" , "Fashion industry (informal)" .)