Budget supermarket left out Brussels for so long (5)
I believe the answer is:
adieu
'for so long' is the definition.
(both can mean goodbye)
'budget supermarket left out brussels' is the wordplay.
'budget supermarket' becomes 'Aldi' (Aldi is a budget supermarket chain).
'left' becomes 'l' (common abbreviation).
'out' indicates named letters should be taken away.
'brussels' becomes 'EU' (European Parliament is based in Brussels).
'aldi' with 'l' taken out is 'adi'.
'adi'+'eu'='ADIEU'
(Other definitions for adieu that I've seen before include "Leave" , "the last word in France" , "left, making this?" , "Farewell to France" , "farewell message" .)