Delves into Spanish cubist to find dirty character (9)
I believe the answer is:
griminess
'dirty character' is the definition.
(quality of being grimy or dirty)
'delves into spanish cubist' is the wordplay.
'delves' becomes 'mines' (as in delving into or mining from something).
'into' means one lot of letters goes inside another.
'spanish cubist' becomes 'gris' (painter Juan Gris, 1887-1927).
'mines' inserted within 'gris' is 'GRIMINESS'.
'to find' is the link.
(Other definitions for griminess that I've seen before include "Amount of muck" , "Quality of coal" .)