Has grown somewhat, but not to maximum extent (4)
I believe the answer is:
owns
'has' is the definition.
('own' can be a synonym of 'have')
'grown somewhat but not to maximum extent' is the wordplay.
'but not to maximum extent' indicates a hidden word (only some of the letters are used).
'OWNS' can be found hidden inside 'grown somewhat'.
(Other definitions for owns that I've seen before include "Confesses" , "Has possession of by right" , "Belongs to" , "Admits possession" , "uses" .)