Dance in Burma, after a fashion (5)
I believe the answer is:
rumba
'dance' is the definition.
(rumba is a type of dance)
'burma after a fashion' is the wordplay.
'after a fashion' is an anagram indicator (letters re-fashioned).
'burma' anagrammed gives 'RUMBA'.
'in' is the link.
(Other definitions for rumba that I've seen before include "South American dance" , "Latin beat" , "Cuban folk-dance" , "One from Cuba" , "number of steps" .)