Might have old dressing? (4)
I believe the answer is:
'dressing?' is the definition.
(I've seen this before)
'might have old' is the wordplay.
'might' becomes 'may' (I've seen this before).
'have' says to put letters next to each other.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
(Other definitions for mayo that I've seen before include "Saucy thing" , "County of Western Eire" , "You'll find it in the Emerald Isle" , "radio presenter" , "Irish county (county town, Castlebar)" .)