Noisiest hooligan going around Delaware Square (7)
I believe the answer is:
loudest
'noisiest' is the definition.
('loud' is associated in meaning with 'noisy')
'hooligan going around delaware square' is the wordplay.
'hooligan' becomes 'lout' (both can mean an aggressive person).
'going around' means one lot of letters goes inside another.
'delaware' becomes 'DE' (standard two letter abbrev).
'square' becomes 's' (abbreviation).
'de'+'s'='des'
'lout' placed around 'des' is 'LOUDEST'.
(Other definitions for loudest that I've seen before include "Noisiest or gaudiest" , "Least restrained" , "Highest in volume" , "Most flashy" , "Most deafening" .)