Cooked last of three dishes perhaps lacking third of meat? (9,4)

'lacking third of meat?' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'cooked last of three dishes' is the wordplay.
I cannot quite see how this works, but
'dishes' could be 'pies' (I've seen this in other clues) and 'pies' is present in the answer.
The remaining letters 'shepherds' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'perhaps' is the link.