How week begins, with caviar for the president (6)
I believe the answer is:
monroe
'president' is the definition.
(I know that Monroe is a president)
'how week begins with caviar' is the wordplay.
'how week begins' becomes 'mon' (short for Monday).
'with' is a charade indicator (letters next to each other).
'caviar' becomes 'roe' (fish eggs).
'mon'+'roe'='MONROE'
'for the' is the link.
(Other definitions for monroe that I've seen before include "Marilyn . . . . . ., tragic Hollywood icon" , "No more the blond film star" , "5th US president, James" , "FILMSTAR" , "See 3" .)