Running Internet without a host (9)
I believe the answer is:
entertain
'host' is the definition.
(thesaurus)
'running internet without a' is the wordplay.
'running' indicates an anagram.
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'internet' with letters rearranged gives 'entertin'.
'entertin' going around 'a' is 'ENTERTAIN'.
(Other definitions for entertain that I've seen before include "Create a diversion" , "Put up" , "can be amusing" , "nurse" , "Amuse - give hospitality" .)