Old man abandoning Spanish dish for this woman (4)
I believe the answer is:
ella
'this woman' is the definition.
(woman's name)
'old man abandoning spanish dish' is the wordplay.
'old man' becomes 'pa' (both can mean someone's father).
'abandoning' suggests deleting specific letters.
'spanish dish' becomes 'paella' (paella is a type of Spanish dish).
'paella' with 'pa' taken out is 'ELLA'.
'for' acts as a link.
(Other definitions for ella that I've seen before include "Woman" , ".... Fitzgerald, late great jazz diva" , "Girl" , "Miss" , "Great late jazz singer . . . . Fitzgerald" .)