The agent admits the general is lethargic (6)
I believe the answer is:
sleepy
'lethargic' is the definition.
(I've seen this before)
'the agent admits the general' is the wordplay.
'the agent' becomes 'spy' (spy is a kind of agent).
'admits' is an insertion indicator.
'the general' becomes 'Lee' (Robert E. Lee - US revolutionary commander).
'spy' going around 'lee' is 'SLEEPY'.
'is' is the link.
(Other definitions for sleepy that I've seen before include "over-tired" , "Drowsy; indolent" , "Ready for bed" , "Feeling like having a snooze" , "Lethargic" .)