Insignificant duke's a weakling (4)
I believe the answer is:
weed
'a weakling' is the definition.
'insignificant duke's' is the wordplay.
'insignificant' becomes 'wee'.
'duke' becomes 'd' (abbreviation).
'wee'+'d'='WEED'
(Other definitions for weed that I've seen before include "Ineffectual person" , "Made water" , "Hoe to remove it" , "Work in garden" , "Went" .)