Chief sobs wildly (4)
I believe the answer is:
boss
'chief' is the definition.
(synonyms)
'sobs wildly' is the wordplay.
'wildly' is an anagram indicator.
'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" .)