Civil engineer on climb becoming bright red (6)
I believe the answer is:
cerise
'bright red' is the definition.
(I've seen this in another clue)
'civil engineer on climb' is the wordplay.
'civil engineer' becomes 'CE' (abbreviation).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'climb' becomes 'rise' (synonyms).
'ce'+'rise'='CERISE'
'becoming' is the link.
(Other definitions for cerise that I've seen before include "Cherry red colour" , "Cherry-coloured" , "EEC, sir, is red" , "Reddish-pink colour" , "Light purplish red" .)