Display greeting in bold inside doorway (7)
I believe the answer is:
exhibit
'display' is the definition.
(synonyms)
'greeting in bold inside doorway' is the wordplay.
'greeting' becomes 'hi' (hi is a kind of greeting).
'in' means one lot of letters goes inside another.
'bold' becomes 'b' (abbreviation).
'inside' indicates putting letters inside.
'doorway' becomes 'exit' (I can't justify this - if you can you should believe this answer much more).
'b' going inside 'exit' is 'exbit'.
'hi' inserted within 'exbit' is 'EXHIBIT'.
Can you help me to learn more?
(Other definitions for exhibit that I've seen before include "Something shown in public" , "Give public show, as of paintings" , "Put on display" , "Manifest" , "Present" .)