Pint? Regularly bleary, Everyman's beginning to tuck in (4)
I believe the answer is:
beer
'pint?' is the definition.
(I've seen this before)
'regularly bleary everyman's beginning to tuck in' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'beginning to' says to take the initial letters.
'tuck in' indicates putting letters inside.
The initial letter of 'everymans' is 'e'.
The alternate letters of 'bleary' are 'ber'.
'ber' going around 'e' is 'BEER'.
(Other definitions for beer that I've seen before include "Drink using hops, malt, etc" , "Stout, for example" , "Drink with a head" , "It may be 13 across-ed!" , "... this at pub?" .)