Emperors brush up outside a party (7)

'emperors' is the definition.
(mikado is a kind of emperor)

'brush up outside a party' is the wordplay.
'brush' becomes 'skim' (both can mean to touch or pass over lightly).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'outside' means one lot of letters goes inside another.
'party' becomes 'do' (do is a kind of party).
'skim' back-to-front is 'miks'.
'a'+'do'='ado'
'miks' placed around 'ado' is 'MIKADOS'.