Present greeting bishop in doorway (7)
I believe the answer is:
exhibit
'present' is the definition.
(I know that present can be written as exhibit)
'greeting bishop in doorway' is the wordplay.
'greeting' becomes 'hi' (hi is a kind of greeting).
'bishop' becomes 'B' (chess abbreviation).
'in' means one lot of letters goes inside another.
'doorway' becomes 'exit' (I am not sure about this - if you are sure you should believe this answer much more).
'hi'+'b'='hib'
'hib' inserted into 'exit' is 'EXHIBIT'.
Can you help me to learn more?
(Other definitions for exhibit that I've seen before include "Something on show" , "Give public show, as of paintings" , "Show - piece of evidence in court" , "Manifest" , "Put on display" .)