Chief sobs wildly (4)
I believe the answer is:
boss
'chief' is the definition.
(I know that chief can be written as boss)
'sobs wildly' is the wordplay.
'wildly' indicates anagramming the letters.
'sobs' with letters rearranged gives 'BOSS'.
(Other definitions for boss that I've seen before include "Person managing" , "Stud; chief" , "excellent American > stud" , "Bully" , "Manager (colloq.); stud" .)