Head covering up party that’s a surprise (4)
I believe the answer is:
hood
'head covering' is the definition.
(I've seen this before)
'up party that's a surprise' is the wordplay.
'up' says the letters should be written backwards (in down clue: letters go upwards).
'party' becomes 'do' (do can informally mean a party).
'that's a surprise' becomes 'oh' (I can't explain this - if you can you should believe this answer much more).
'do'+'oh'='dooh'
'dooh' back-to-front is 'HOOD'.
Can you help me to learn more?
(Other definitions for hood that I've seen before include "Head covering of an American gangster" , "See 8" , "Capital cover" , "Part of subfusc" , "Cover - American gangster - Robin?" .)