I would have gone running out to get him (6)
I believe the answer is:
gideon
'him' is the definition.
'i would have gone running out' is the wordplay.
'would have' becomes 'd' (I've seen this in other clues).
'running' indicates an anagram.
'out' means one lot of letters goes inside another.
'gone' is an anagram of 'geon'.
'i'+'d'='id'
'id' placed into 'geon' is 'GIDEON'.
'to get' acts as a link.
(Other definitions for gideon that I've seen before include "Biblical hero" , "Israelite leader against Midianites" , "Israel judge; hotel bible" , "Israelite hero" , "Israelite leader; I'd gone (anag.)" .)