After second sight, notice inside lane was a walkway (9)
I believe the answer is:
esplanade
'a walkway' is the definition.
(esplanade is a kind of walkway)
'after second sight notice inside lane' is the wordplay.
'after' says to put letters next to each other.
'second sight' becomes 'esp' (extrasensory perception).
'notice' becomes 'ad' (both can mean an advertisement).
'inside' is an insertion indicator.
'ad' put within 'lane' is 'lanade'.
'esp' put next to 'lanade' is 'ESPLANADE'.
'was' acts as a link.
(Other definitions for esplanade that I've seen before include "Seafront walkway" , "Level seashore walkway" , "prom" , "Long wide pavement next to a beach" , "Walkway beside the seashore" .)