Perhaps Shakespeare eats no meals (5)
I believe the answer is:
board
'meals' is the definition.
(I've seen this before)
'perhaps shakespeare eats no' is the wordplay.
'perhaps shakespeare' becomes 'bard'.
'eats' means one lot of letters goes inside another.
'no' becomes 'o' (resembles 0 - 'no' can mean 'zero').
'bard' enclosing 'o' is 'BOARD'.
(Other definitions for board that I've seen before include "panel" , "Live in lodgings" , "Directors' group" , "See 21 Down" , "provisioning of meals" .)