Club in Corsica performs a balancing act (10)
I believe the answer is:
acrobatics
'a balancing act' is the definition.
'acrobatics' can be an answer for 'act' (acrobatics is a kind of act). I am not sure about the 'a balancing' bit.
'club in corsica performs' is the wordplay.
'club' becomes 'bat' (I've seen this before).
'in' means one lot of letters goes inside another.
'performs' indicates anagramming the letters.
'corsica' is an anagram of 'acroics'.
'bat' going inside 'acroics' is 'ACROBATICS'.
Can you help me to learn more?
(Other definitions for acrobatics that I've seen before include "What one may see in circus" , "pursuit of tumblers" .)