Tea dance (a third one) (4)
I believe the answer is:
chai
'tea' is the definition.
(I've seen this before)
'dance a third one' is the wordplay.
'dance a third' becomes 'cha' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'one' becomes 'i' (Roman numeral).
'cha'+'i'='CHAI'
Can you help me to learn more?
(Other definitions for chai that I've seen before include "Form of tea" , "lady" .)