Mess up a hairstyle, having a broken leg (6)
I believe the answer is:
Here is my best explanation:
'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'.
(Other definitions for bungle that I've seen before include "(Make an) embarrassing mistake", "Botch; failure", "Badly handle", "Make a mess of", "Botch, make a hames of", "Make a hash of the job", "Mess up", "Tackle clumsily and fail", "Clumsy mistake" and "Do something carelessly or badly".)