Lightheartedness is the thing sought in duty (6)
I believe the answer is:
levity
'lightheartedness' is the definition.
(thesaurus)
'sought in duty' is the wordplay.
'sought' becomes 'it' (I can't explain this - if you can you should give a lot more credence to this answer).
'in' means one lot of letters goes inside another.
'duty' becomes 'levy' (I've seen this in another clue).
'it' going within 'levy' is 'LEVITY'.
'is the thing' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for levity that I've seen before include "thoughtlessness" , "lack of respect" , "Unseriousness" , "Disrespectful humour" , "Light-heartedness" .)