One minds young graduate being next to model (4-6)
I believe the answer is:
'one minds young' is the definition.
(baby-sitters look after children)
'graduate being next to model' is the wordplay.
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'being next to' becomes 'by'.
'model' becomes 'sitter' (I've seen this before).