To extend my range as Duke, I write poetry (9)
I believe the answer is:
diversify
'to extend my range' is the definition.
(as in diversifying one's activities)
'duke i write poetry' is the wordplay.
'duke' becomes 'd' (abbreviation).
'write poetry' becomes 'versify' (I've seen this before).
'd'+'i'+'versify'='DIVERSIFY'
'as' acts as a link.
(Other definitions for diversify that I've seen before include "To do something different" , "Become more varied" .)