Relative, after small wild deer, strolled (9)
I believe the answer is:
sauntered
'strolled' is the definition.
('saunter' can be a synonym of 'stroll')
'relative after small wild deer' is the wordplay.
'relative' becomes 'aunt' (aunt is a type of relative).
'after' is a charade indicator (letters next to each other).
'small' becomes 's' (abbreviation - e.g. clothes size).
'wild' indicates anagramming the letters.
'deer' with letters rearranged gives 'ered'.
'aunt' put after 's' is 'saunt'.
'saunt'+'ered'='SAUNTERED'
(Other definitions for sauntered that I've seen before include "Walked slowly" , "Strolled" .)