Bound to be appreciative (7)
I believe the answer is:
obliged
I believe this clue is a double definition.
'bound' is the first definition.
('oblige' can be a synonym of 'bind')
'be appreciative' is the second definition.
(thesaurus)
'to' acts as a link.
(Other definitions for obliged that I've seen before include "Constrained" , "Compelled by duty" , "Did favour to, or coerced" , "Morally or legally bound (to do something)" , "Bound by a favour rendered" .)