Walk having a street directory (6)
I believe the answer is:
stroll
'walk' is the definition.
(strolling is a kind of walking)
'a street directory' is the wordplay.
'a street' becomes 'st' (abbreviation).
'directory' becomes 'roll' (I've seen this before).
'st'+'roll'='STROLL'
'having' is the link.
(Other definitions for stroll that I've seen before include "A casual, relaxing walk" , "cinch" , "gentle pace" , "Amble or ramble" , "A casual or lazy walk" .)