Put fence round space nearby (7)
I believe the answer is:
enclose
'put fence round' is the definition.
(enclose within fences)
'space nearby' is the wordplay.
'space' becomes 'en' (in printing, a space as wide as a letter 'n').
'nearby' becomes 'close' (similar in meaning).
'en'+'close'='ENCLOSE'
(Other definitions for enclose that I've seen before include "Put inside" , "Hem in" , "Surround; place in envelope (with letter)" , "Confine" , "Surround on all sides" .)