I desert East Anglian city angrily (7)
I believe the answer is:
irately
'angrily' is the definition.
(I've seen this in another clue)
'i desert east anglian city' is the wordplay.
'desert' becomes 'rat' (abandon treacherously).
'east anglian city' becomes 'ely' (I've seen this before).
'i'+'rat'+'ely'='IRATELY'
(Other definitions for irately that I've seen before include "Angrily" , "With great anger" , "Cross style" .)