Cheers, cheers and cheerio (2-2)
I believe the answer is:
ta-ta
'cheerio' is the definition.
(I've seen this before)
'cheers cheers' is the wordplay.
'cheers' becomes 'ta' (both can informally mean thank you).
'cheers' becomes 'ta' (both can informally mean thank you).
'ta'+'ta'='TA-TA'
'and' is the link.
(Other definitions for ta-ta that I've seen before include "Adieu" , "Bye-bye" , "Bye!" , "A Farewell" , "Cheerio" .)