Protest when flipping Everyman welcomed into party (4)
I believe the answer is:
demo
'protest' is the definition.
(demonstration)
'flipping everyman welcomed into party' is the wordplay.
'flipping' shows that the letters should be reversed in order.
'everyman' becomes 'me' (where the crossword setter is 'Everyman').
'welcomed into' means one lot of letters goes inside another.
'party' becomes 'do' (do can informally mean a party).
'me' backwards is 'em'.
'em' inserted into 'do' is 'DEMO'.
'when' is the link.
(Other definitions for demo that I've seen before include "Protest march (sl.)" , "Public protest meeting" , "Political protest" , "illustration" , "Show" .)