ESP in later years keeps old in hush-hush work (9)
I believe the answer is:
espionage
'hush-hush work' is the definition.
(I've seen this before)
'esp in later years keeps old' is the wordplay.
'later years' becomes 'age' (old age).
'keeps' indicates putting letters inside.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'in'+'age'='inage'
'inage' going around 'o' is 'ionage'.
'esp'+'ionage'='ESPIONAGE'
'in' is the link.
(Other definitions for espionage that I've seen before include "seeking information" , "intelligence" , "Practice of spying" , "secret work" , "undercover work" .)