Former opener for Essex enters punctually (3-4)
I believe the answer is:
one-time
'former' is the definition.
(I know that former can be written as one-time)
'opener for essex enters punctually' is the wordplay.
'opener for' suggests taking the first letters.
'enters' indicates putting letters inside.
'punctually' becomes 'on time' (I've seen this in another clue).
The first letter of 'essex' is 'e'.
'e' inserted into 'ontime' is 'ONE-TIME'.
(Other definitions for one-time that I've seen before include "Former" , "Relating to a single occasion" .)