Succeeded also daily - that's abrasive (9)
I believe the answer is:
sandpaper
'that's abrasive' is the definition.
(sandpaper is a kind of abrasive)
'succeeded also daily' is the wordplay.
'succeeded' becomes 's' (genealogical abbreviation).
'also' becomes 'and' (both can mean in addition).
'daily' becomes 'paper' (newspaper).
's'+'and'+'paper'='SANDPAPER'
(Other definitions for sandpaper that I've seen before include "Material used for smoothing" , "Abrasive material" , "Means of smoothing wood" , "Abrasive sheet (DIY)" , "Abrasive smoother" .)