Rumba dancing in part of Asia, once (5)
I believe the answer is:
burma
'part of asia once' is the definition.
(former name of Myanmar)
'rumba dancing' is the wordplay.
'dancing' indicates an anagram.
'rumba' is an anagram of 'BURMA'.
'in' acts as a link.
(Other definitions for burma that I've seen before include "It's now called Myanmar" , "Country of SE Asia" , "Country also known as Myanmar" , "Myanmar, formerly" , "Country whose name was changed to Myanmar in 1989" .)