Greeting Henry with hot drink outside (9)
I believe the answer is:
handshake
'greeting' is the definition.
(thesaurus)
'henry with hot drink outside' is the wordplay.
'henry' becomes 'h' ('H' can be a synonym of 'henry').
'with' becomes 'and' (I've seen this before).
'hot drink outside' becomes 'shake' (I can't explain this - if you can you should give a lot more credence to this answer).
'h'+'and'+'shake'='HANDSHAKE'
(Other definitions for handshake that I've seen before include "A link" , "Form of greeting" , "Conventional sort of manual greeting" , "Gesture of greeting or of agreeing a deal" , "Conventional greeting of manual kind" .)