Everyman’s after a hostelry in Italian port (4)
I believe the answer is:
bari
'italian port' is the definition.
(I've seen this in another clue)
'everyman's after a hostelry' is the wordplay.
'everyman' becomes 'i' (where 'Everyman' is the setter of the crossword).
'after' means one lot of letters go next to another.
'a hostelry' becomes 'bar' (I've seen this before).
'i' after 'bar' is 'BARI'.
'in' is the link.
(Other definitions for bari that I've seen before include "Adriatic seaport" , "Adriatic resort" , "Adriatic port" .)