Bishop and President having a tot (4)
I believe the answer is:
babe
'a tot' is the definition.
(I've seen this in another clue)
'bishop and president' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'and' is a charade indicator (letters next to each other).
'president' becomes 'abe' (Abraham (Abe) Lincoln).
'b'+'abe'='BABE'
'having' is the link.
(Other definitions for babe that I've seen before include "Tiny child" , "Youngster" , "Very young child (often found in arms)" , "good-looking young lady" , "Ruth, for example" .)