Greatest duty is essentially to lead the largest number (6)
I believe the answer is:
'greatest' is the definition.
(I've seen this before)
'duty is essentially to lead the largest number' is the wordplay.
'is essentially' indicates the central letters.
'to lead' means one lot of letters go next to another.
'the largest number' becomes 'most' (I can't explain this - if you can you should believe this answer much more).
The middle letters of 'duty' are 'ut'.
Can you help me to learn more?
(Other definitions for utmost that I've seen before include "Maximum effort" , "At furthest limit" , "Furthest or maximum possible" , "last" , "Furthest or extreme" .)