Maybe Rupert Everett's heading inside pub (4)
I believe the answer is:
bear
'maybe rupert' is the definition.
(I know that Rupert Bear is a bear)
'everett's heading inside pub' is the wordplay.
'heading' indicates taking the first letters (head could mean the top letter).
'inside' is an insertion indicator.
'pub' becomes 'bar' (both are drinking establishments).
The first letter of 'everett' is 'e'.
'e' going into 'bar' is 'BEAR'.
(Other definitions for bear that I've seen before include "stomach and > suffer" , "Endure - mammal" , "Huge carnivore" , "Support; share seller" , "Carry - teddy" .)