Fairy that's mischievous: clean her up (10)
I believe the answer is:
leprechaun
'fairy' is the definition.
(leprechaun is a kind of fairy)
'mischievous clean her up' is the wordplay.
'mischievous' is an anagram indicator.
'clean'+'her'+'up'='cleanherup'
'cleanherup' anagrammed gives 'LEPRECHAUN'.
'that's' acts as a link.
(Other definitions for leprechaun that I've seen before include "He helps Irish housewife" , "Mischievous imp" , "Elf in Irish folklore" , "Mischievous Irish elf" , "Mischievous Irish sprite" .)