Award given to one in pigpen displaying corpulence (7)
I believe the answer is:
obesity
'corpulence' is the definition.
(I know that corpulence can be written as obesity)
'award given to one in pigpen' is the wordplay.
'award' becomes 'OBE' (Order of the British Empire).
'given to' is a charade indicator (letters next to each other).
'one' becomes 'i' (Roman numeral).
'in' is an insertion indicator.
'pigpen' becomes 'sty' (synonyms).
'i' inserted within 'sty' is 'sity'.
'obe'+'sity'='OBESITY'
'displaying' is the link.
(Other definitions for obesity that I've seen before include "It obeys, being much too fat" , "Fatness to great excess" , "Excessive and unhealthy fatness" , "health issue" , "State of being unhealthily fat" .)