Support son entering Bar with little hesitation (7)
I believe the answer is:
bolster
'support' is the definition.
(synonyms)
'son entering bar with little hesitation' is the wordplay.
'son' becomes 's'.
'entering' means one lot of letters goes inside another.
'bar' becomes 'bolt' (bolt is a kind of bar).
'with' says to put letters next to each other.
'little hesitation' becomes 'er' (expression of hesitation).
's' put into 'bolt' is 'bolst'.
'bolst'+'er'='BOLSTER'
(Other definitions for bolster that I've seen before include "Lobster (anag.)" , "support for head after retiring" , "Provide reinforcement" , "Strengthen - long pillow" , "Long thick pillow" .)