Admit one criminal with influence (8)
I believe the answer is:
dominate
'influence' is the definition.
(dominating is a kind of influencing)
'admit one criminal' is the wordplay.
'criminal' indicates anagramming the letters.
'admit'+'one'='admitone'
'admitone' anagrammed gives 'DOMINATE'.
'with' is the link.
(Other definitions for dominate that I've seen before include "Admit one in order to be in control" , "Tower over" , "corner" , "Be lord over" , "Rule" .)