Great hints clean up one’s act (10,3)
I believe the answer is:
straighten out
'great hints clean up one's act' is the definition.
I can't judge whether this definition defines the answer.
'clean up one's act' is the wordplay.
'clean up' becomes 'straighten' (synonyms).
'one's act' becomes 'out' (I can't justify this - if you can you should believe this answer much more).
'straighten'+'out'='STRAIGHTEN OUT'
Can you help me to learn more?
(Another definition for straighten out that I've seen is " Resolve, disentangle".)