Woman makes a mud pie (4)
I believe the answer is:
maud
'woman' is the definition.
(woman's name)
'a mud pie' is the wordplay.
'pie' indicates an anagram.
'a'+'mud'='amud'
'amud' with letters rearranged gives 'MAUD'.
'makes' is the link.
(Other definitions for maud that I've seen before include "Tennyson poem" , "Girl invited into the garden in song" , "Come into the garden, - (Tennyson)" , "Girl invited into garden (Tennyson)" , "Old song: ''Come into the garden . . . .''" .)