Loose woman cut short wife in Essex town (6)
I believe the answer is:
harlow
'essex town' is the definition.
(I've seen this before)
'loose woman cut short wife' is the wordplay.
'loose woman' becomes 'harlot' (I've seen this in another clue).
'cut short' means to remove the last letter.
'wife' becomes 'w'.
'harlot' with its last letter taken away is 'harlo'.
'harlo'+'w'='HARLOW'
'in' acts as a link.
(Other definitions for harlow that I've seen before include "Essex town - American film actress, d. 1937" , "Blonde bombshell" , "FILMSTAR" , "place in Essex" , "Jean ---, actress; Essex new town" .)