It means the opposite to Cleopatra's mate, Mike (7)
I believe the answer is:
antonym
'it means the opposite' is the definition.
(I've seen this before)
'cleopatra's mate mike' is the wordplay.
'cleopatra's mate' becomes 'antony' (I am not sure about this - if you are sure you should believe this answer much more).
'mike' becomes 'M' (phonetic alphabet: alpha, bravo, charlie etc.).
'antony'+'m'='ANTONYM'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for antonym that I've seen before include "A word's opposite" , "Nick's could be free" , "opposing term" , "A word opposite in meaning to another" , "As 'happy' is to 'sad' or 'long' to 'short'" .)