Better garden party? (5)
I believe the answer is:
'better' is the definition.
(to outdo is to beat or do better than)
'garden party?' is the wordplay.
'garden' becomes 'out' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'party?' becomes 'do' (do can informally mean a party).
Can you help me to learn more?
(Other definitions for outdo that I've seen before include "Surpass, go one better than" , "Overcome" , "Go one beter than, surpass" , "Defeat" , "Eclipse" .)