Quietly, a violin's playing in exhibition building (8)
I believe the answer is:
pavilion
'exhibition building' is the definition.
(I've seen this before)
'quietly a violin's playing' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'playing' is an anagram indicator.
'violin' with letters rearranged gives 'vilion'.
'p'+'a'+'vilion'='PAVILION'
'in' is the link.
(Other definitions for pavilion that I've seen before include "hospital block" , "Exhibition tent; sports building" , "Cricket ground clubhouse" , "Cricket ground building" , "Large and often sumptuous tent" .)