Light in city initially niggled bird (7)
I believe the answer is:
lantern
'light' is the definition.
(lantern is a type of light)
'city initially niggled bird' is the wordplay.
'city' becomes 'LA' (Los Angeles).
'initially' indicates taking the first letters.
'bird' becomes 'tern' (tern is a kind of bird).
The initial letter of 'niggled' is 'n'.
'la'+'n'+'tern'='LANTERN'
'in' acts as a link.
(Other definitions for lantern that I've seen before include "Light-admitting structure on roof" , "Enclosed lamp" , "Transparent case for candle" , "Light in a protective casing" , "Portable lamp case" .)