Delicacy that's unlimited if in Essex (7)
I believe the answer is:
finesse
'delicacy' is the definition.
('finesse' can be a synonym of 'delicacy')
'unlimited if in essex' is the wordplay.
'unlimited' says the answer is hidden in the clue (the answer is currently being held or limited).
'FINESSE' is hidden within 'if in essex'.
'that's' acts as a link.
(Other definitions for finesse that I've seen before include "subtle tactic" , "Achieve with subtlety and skill" , "Artifice" , "Subtle skill; bridge ploy" , "Refinement" .)