Crazy upper-class twit discharged in US city (5)
I believe the answer is:
nutty
'crazy' is the definition.
(I've seen this before)
'upper-class twit discharged in us city' is the wordplay.
'upper-class' becomes 'u' (similar in meaning).
'discharged' suggests removing the centre (the letters inside the word released or discharged).
'in' indicates putting letters inside.
'us city' becomes 'NY' (abbreviation for New York).
'twit' with its centre taken out is 'tt'.
'u'+'tt'='utt'
'utt' inserted into 'ny' is 'NUTTY'.
(Other definitions for nutty that I've seen before include "Mad - with small pieces of coal" , "Eccentric - like nougat?" , "passionate" , "Crackers" , "Like, eg, brazils" .)