Dig succeeded, turning up bit of debris (4)
I believe the answer is:
spud
'dig' is the definition.
(spud can mean to dig up in the garden)
'succeeded turning up bit of debris' is the wordplay.
'succeeded' becomes 's' (genealogical abbreviation).
'turning' is a reversal indicator.
'bit of' indicates taking the first letters.
The initial letter of 'debris' is 'd'.
'up' reversed gives 'pu'.
's'+'pu'+'d'='SPUD'
(Other definitions for spud that I've seen before include "Potato (colloq.)" , "Weed spade" , "One might have an eye" , "The humble colloquial potato" , "King Edward, say (slang)" .)