Exhibit female pig swallowing hard (4)
I believe the answer is:
show
'exhibit' is the definition.
(I know that exhibit is a kind of show)
'female pig swallowing hard' is the wordplay.
'female pig' becomes 'sow' (I've seen this in another clue).
'swallowing' indicates putting letters inside.
'hard' becomes 'h' (abbreviation used in pencil classifications).
'sow' going around 'h' is 'SHOW'.
(Other definitions for show that I've seen before include "The world of entertainment" , "Entertainment - guide" , "Point out - parade" , "Expose" , "Musical featuring 'Old Man River'" .)