Strolled like true Danes, perhaps (9)
I believe the answer is:
sauntered
'strolled' is the definition.
('saunter' can be a synonym of 'stroll')
'true danes perhaps' is the wordplay.
'perhaps' indicates an anagram.
'true'+'danes'='truedanes'
'truedanes' anagrammed gives 'SAUNTERED'.
'like' acts as a link.
(Other definitions for sauntered that I've seen before include "Strolled" , "Walked slowly" .)