Moon cheers, a little bit (4)
I believe the answer is:
iota
'a little bit' is the definition.
(I've seen this in another clue)
'moon cheers' is the wordplay.
'moon' becomes 'Io' (moon of Jupiter).
'cheers' becomes 'ta' (both can informally mean thank you).
'io'+'ta'='IOTA'
(Other definitions for iota that I've seen before include "Grain" , "Greek letter - small quantity" , "Gk. letter; tiny amount" , "Contrivance" , "Tiny bit" .)