The writer’s keeping on meeting mischievous royalty? (8)
I believe the answer is:
monarchy
'royalty?' is the definition.
(monarchs are royal)
'the writer's keeping on meeting mischievous' is the wordplay.
'the writer's' becomes 'my' (belonging to the person who set the crossword).
'keeping' indicates putting letters inside (some letters kept inside).
'meeting' means one lot of letters go next to another.
'mischievous' becomes 'arch' (arch can mean mischievous or playful).
'on'+'arch'='onarch'
'my' placed around 'onarch' is 'MONARCHY'.
(Other definitions for monarchy that I've seen before include "sort of government" , "kind of government" , "Rule by a sovereign" , "Rule by a king or queen" , "Sovereign state" .)