Vivacity of English knight touring US city (4)
I believe the answer is:
elan
'vivacity' is the definition.
(I've seen this in another clue)
'english knight touring us city' is the wordplay.
'english' becomes 'E' (abbreviation as in OED).
'knight' becomes 'n' (chess abbreviation).
'touring' means one lot of letters goes inside another (touring can mean going round).
'us city' becomes 'LA' (Los Angeles).
'e'+'n'='en'
'en' going around 'la' is 'ELAN'.
'of' acts as a link.
(Other definitions for elan that I've seen before include "Dash, style" , "Stylish elegance" , "Stylishness" , "Stylish enthusiasm" , "Grass with edible grains" .)