Art institution's communications palaver (5)
I believe the answer is:
prado
'art institution's' is the definition.
(Museo del Prado in Spain)
'communications palaver' is the wordplay.
'communications' becomes 'PR' (public relations).
'palaver' becomes 'ado' (both can mean a fuss).
'pr'+'ado'='PRADO'
(Other definitions for prado that I've seen before include "picture-house" , "Madrid museum" , "gallery for paintings" , "foreign gallery" , "exhibits here?" .)