Gallery disposing of European rubbish (3)
I believe the answer is:
tat
'rubbish' is the definition.
(low-quality items or material)
'gallery disposing of european' is the wordplay.
'gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'disposing of' is a deletion indicator.
'european' becomes 'E' (abbreviation e.g. EU).
'tate' with 'e' removed is 'TAT'.
(Other definitions for tat that I've seen before include "Tawdry and shabby article" , "What you get for tit" , "Shoddy stuff (colloq.)" , "Tawdry or shabby articles" , "Worthless items" .)