My pet Dicky is hungry (5)
I believe the answer is:
empty
'hungry' is the definition.
(similar in meaning)
'my pet dicky' is the wordplay.
'dicky' indicates anagramming the letters (dicky can mean not functioning properly).
'my'+'pet'='mypet'
'mypet' anagrammed gives 'EMPTY'.
'is' is the link.
(Other definitions for empty that I've seen before include "Devoid of content" , "Cleared out" , "Unoccupied" , "Vacuous" , "left for the milkman?" .)