Perform better than head of party, dividing cost (7)
I believe the answer is:
outplay
'perform better' is the definition.
(to outplay someone is to perform better than them)
'head of party dividing cost' is the wordplay.
'head of' becomes 'out' (I can't justify this - if you can you should give a lot more credence to this answer).
'party' becomes 'l'.
'dividing' indicates putting letters inside (inserted letters divide the word).
'cost' becomes 'pay' (pay is a kind of cost).
'l' inserted inside 'pay' is 'play'.
'out'+'play'='OUTPLAY'
'than' is the link.
Can you help me to learn more?
(Other definitions for outplay that I've seen before include "As sportsperson, overcome" , "Act better" , "Defeat (sport)" , "Perform better than" , "Excel at games" .)