Cite former vice president's outside choice (10)
I believe the answer is:
preference
'choice' is the definition.
(I know that preference is a type of choice)
'cite former vice president's outside' is the wordplay.
'cite' becomes 'refer' (I've seen this in another clue).
'former vice president' becomes 'Pence' (former US vice president Mike Pence).
'outside' is an insertion indicator.
'refer' inserted within 'pence' is 'PREFERENCE'.
(Other definitions for preference that I've seen before include "Liking for one thing more than another" , "Predilection, penchant" , "what's valued higher" , "Bent" , "favourite" .)