Essentially, tenanting a pigpen's offensive (5)
I believe the answer is:
nasty
'offensive' is the definition.
(I've seen this before)
'essentially tenanting a pigpen's' is the wordplay.
'essentially' indicates the central letters.
'pigpen' becomes 'sty' (synonyms).
The middle of 'tenanting' is 'n'.
'n'+'a'+'sty'='NASTY'
(Other definitions for nasty that I've seen before include "Horrible" , "Filthy" , "Awful" , "Disagreeable" , "Horrid, repugnant" .)