Black mark getting start of the sum wrong (4)
I believe the answer is:
smut
'black' is the definition.
(thesaurus)
'getting start of the sum wrong' is the wordplay.
'getting' is a charade indicator (letters next to each other).
'start of' says to take the initial letters.
'wrong' is an anagram indicator.
The initial letter of 'the' is 't'.
'sum' anagrammed gives 'smu'.
't' after 'smu' is 'SMUT'.
'mark' is the link.
(Other definitions for smut that I've seen before include "Lewd material" , "Obscene material" , "Small flake of dirt" , "Smudge of soot" , "porn?" .)