Shame! Mine's the fourth of July! (4)
I believe the answer is:
pity
'shame' is the definition.
('pity' can be a synonym of 'shame')
'mine's the fourth of july' is the wordplay.
'mine' becomes 'pit' (down the pit**).
'the fourth of july' becomes 'y' (fourth letter of the word 'July').
'pit'+'y'='PITY'
(Other definitions for pity that I've seen before include "Sympathy for others" , "Sympathise with" , "Feel sorry for" , "Crying shame" , "Mercy" .)