“Bazaar” earnestly covers this subject (4)
I believe the answer is:
area
'this subject' is the definition.
(area is a kind of subject)
'bazaar earnestly covers' is the wordplay.
'covers' indicates the answer is hidden within the clue (I've seen 'covering' mean this).
'AREA' can be found hidden inside 'bazaar earnestly'.
(Other definitions for area that I've seen before include "The measure of a surface" , "Locality" , "Length multiplied by breadth" , "Extent of a two-dimensional surface" , "Expanse of a surface" .)