Depend on entirely, not half! (4)
I believe the answer is:
rely
'depend' is the definition.
(to depend on someone is to rely on them)
'entirely? not half' is the wordplay.
'not half' means to take half the letters.
'entirely' halved is 'RELY'.
'on' is the link.
(Other definitions for rely that I've seen before include "Be sure" , "Have confidence or faith in" , "City with cathedral" , "Lyre (anag.)" , "Depend confidently (on)" .)