She has half a mind to go by motorway (4)
I believe the answer is:
mimi
'she' is the definition.
'half a mind to go by motorway' is the wordplay.
'half a' suggests halving the letters.
'to go by' is a charade indicator (letters next to each other).
'motorway' becomes 'MI' (resembles M1, English motorway).
'mind' halved is 'mi'.
'mi'+'mi'='MIMI'
'has' is the link.
(Other definitions for mimi that I've seen before include "Her tiny hand was frozen (Puccini)" , "Bohemian girl" , "showgirl" , "'They call me - - ' , (Lucia)" , "Starving character of "La Boheme"" .)