Terribly tiring backing Brussels plot (8)
I believe the answer is:
intrigue
'plot' is the definition.
(intrigue is a kind of plot)
'terribly tiring backing brussels' is the wordplay.
'terribly' indicates an anagram.
'backing' is a reversal indicator.
'brussels' becomes 'eu' (Brussels is a metonym for the European Union).
'eu' written backwards gives 'ue'.
'tiring' anagrammed gives 'intrig'.
'intrig'+'ue'='INTRIGUE'
(Other definitions for intrigue that I've seen before include "Plot in underhand way" , "Secret plotting" , "An underhand plot or conspiracy" , "Underhand scheming" , "liaison" .)