See how day developed with make-up (9)
I believe the answer is:
eyeshadow
'make-up' is the definition.
(I know that eyeshadow is a type of makeup)
'see how day developed' is the wordplay.
'developed' indicates anagramming the letters.
'see'+'how'+'day'='seehowday'
'seehowday' is an anagram of 'EYESHADOW'.
'with' is the link.
(Other definitions for eyeshadow that I've seen before include "cosmetic" , "application to viewers" , "used to put dark side into orbit" , "Face application" , "beauty aid" .)