Managed to proceed, reaching Burmese city (7)
I believe the answer is:
rangoon
'burmese city' is the definition.
'Rangoon' can be an answer for 'city' (Rangoon is an example). I'm not certain of the 'burmese' bit.
'managed to proceed' is the wordplay.
'managed' becomes 'ran' (both can mean organised or was in charge of).
'to proceed' becomes 'go on' ('go on' can be a synonym of 'proceed').
'ran'+'goon'='RANGOON'
'reaching' is the link.
Can you help me to learn more?
(Other definitions for rangoon that I've seen before include "old Asian city" , "Port and largest city of Burma" , "Former capital of Burma" , "Asian capital" , "Burma's capital" .)