City path starts off with three directions (6)
I believe the answer is:
athens
'city' is the definition.
(Athens is an example)
'path starts off with three directions' is the wordplay.
'three directions' means three substitutions for 'direction'.
'starts off' means to remove the first letter (I've seen 'starting off' mean this (the starting letter is removed)).
'with' is a charade indicator (letters next to each other).
'direction' becomes 'E' (E is an example).
'direction' becomes 'N' (N is an example).
'direction' becomes 's' (S is an example).
'path' with its first letter taken away is 'ath'.
'ath'+'e'+'n'+'s'='ATHENS'
(Other definitions for athens that I've seen before include "Hasten to the Hellenic city" , "foreign city" , "Plato's birthplace" , "City in which 13 Across founded school" , "Hasten to European capital" .)