Get by policeman close to entrance (4)
I believe the answer is:
cope
'get by' is the definition.
('cope' can be a synonym of 'get by')
'policeman close to entrance' is the wordplay.
'policeman' becomes 'cop' (I've seen this before).
'close to' suggests the final letters (the close/ending of).
The last letter of 'entrance' is 'e'.
'cop'+'e'='COPE'
(Other definitions for cope that I've seen before include "Long cloak for a priest" , "Manage - poet, first name 18" , "Rise to the occasion" , "Deal with, manage successfully" , "special cloak" .)