Due to corruption, reposting my last message ...
I would also have had a first reaction of MIME and was impressed with PaulineP's suggestion of MUMS.
'Mu' is a phonetic rendition of the greek letter, whereas 'i' and 'e' are not which is why MIME wouldn't works so well
as MUMS (in my opinion). Also, as C points out, the apostrophe isn't after the 's'.
Assuming that MUMS is the correct answer, then the clue ... Greek character's given thousands to act in play (4) ... seems to me to work ok in that it means a greek
character (MU) is to be appended by thousands (MS).