The master has sweetheart – name her! (3)
I believe the answer is:
mae
'her' is the definition.
'the master has sweetheart' is the wordplay.
'the master' becomes 'ma'.
'has' means one lot of letters go next to another.
'sweetheart' becomes 'e' (the heart/centre of 'sweet'**).
'ma'+'e'='MAE'
'name' is the link.
This may not be right. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for mae that I've seen before include "The first Hollywood blonde femme fatale, . . . West" , "Girl" , "Woman" , "- - West, movie vamp" , "- - West, life-jacket" .)