Half open? Near – shut in (7)
I believe the answer is:
enclose
'shut in' is the definition.
(synonyms)
'half open? near' is the wordplay.
'half' means to take half the letters.
'near' becomes 'close' (synonyms).
'open' halved is 'en'.
'en'+'close'='ENCLOSE'
(Other definitions for enclose that I've seen before include "Fence in (common land)" , "embrace" , "Confine" , "Surround; place in envelope (with letter)" , "Include N pen" .)