Mess up a hairstyle, having a broken leg (6)
I believe the answer is:
bungle
'mess up' is the definition.
('bungle' can be a synonym of 'mess up')
'a hairstyle having a broken leg' is the wordplay.
'a hairstyle' becomes 'bun'.
'having' means one lot of letters go next to another.
'a broken' is an anagram indicator.
'leg' with letters rearranged gives 'gle'.
'bun'+'gle'='BUNGLE'
(Other definitions for bungle that I've seen before include "Make a hash of the job" , "Botch; failure" , "Badly handle" , "Make a mess of" , "Do something carelessly or badly" .)