Bound to vary diet (4)
I believe the answer is:
tied
'bound' is the definition.
(similar in meaning)
'vary diet' is the wordplay.
'vary' indicates an anagram.
'diet' anagrammed gives 'TIED'.
'to' acts as a link.
(Other definitions for tied that I've seen before include "(Of pub) controlled by a brewery" , "Bound or secured" , "Fastened with string" , "Restricted, bound" , "limited" .)