Dogged, check this compiler's crossword, finally (10)
I believe the answer is:
determined
'dogged' is the definition.
(thesaurus)
'check this compiler's crossword finally' is the wordplay.
'check' becomes 'deter' (slow the progress of).
'this compiler's' becomes 'mine' (belonging to the crossword compiler).
'finally' suggests the final letters.
The last letter of 'crossword' is 'd'.
'deter'+'mine'+'d'='DETERMINED'
(Other definitions for determined that I've seen before include "settled" , "Resolved" , "Found out" , "With full strength and concentration" , "Decided - resolute" .)