Getting rid of doughy pudding left abandoned (7)
I believe the answer is:
dumping
'getting rid of' is the definition.
(dumping is a kind of getting rid of)
'doughy pudding left abandoned' is the wordplay.
'doughy pudding' becomes 'dumpling'.
'left' becomes 'l' (common abbreviation).
'abandoned' is a deletion indicator.
'dumpling' with 'l' taken out is 'DUMPING'.
(Other definitions for dumping that I've seen before include "Dropping" , "Disposing of" .)