She has half a mind to make another appearance (4)
I believe the answer is:
mimi
'she' is the definition.
'half a mind to make another appearance' is the wordplay.
'half a' suggests halving the letters.
'to make another appearance' becomes 'mi' (I am not sure about this - if you are sure you should believe this answer much more).
'mind' with half the letters taken is 'mi'.
'mi'+'mi'='MIMI'
'has' is the link.
Can you help me to learn more?
(Other definitions for mimi that I've seen before include "Starving character of "La Boheme"" , "I'm, I'm mad about the heroine in 'La Boheme'" , "Puccini's seamstress" , "Tragic heroine" , "La Boheme character (whose tiny hand is frozen)" .)