Essex empty, partly free from obligation (6)
I believe the answer is:
exempt
'free from obligation' is the definition.
(I've seen this before)
'essex empty partly' is the wordplay.
'partly' indicates a hidden word.
'EXEMPT' is hidden within 'essex empty'.
(Other definitions for exempt that I've seen before include "Privileged" , "Absolve, excuse" , "Freed from obligation, tax etc" , "Absolved" , "Excused - let off" .)