Dog had Miss Piggy brought round? (6)
I believe the answer is:
shadow
'dog' is the definition.
(I've seen this before)
'had miss piggy brought round?' is the wordplay.
'miss piggy' becomes 'sow' (a sow is a female pig).
'brought round?' is an insertion indicator.
'had' inserted into 'sow' is 'SHADOW'.
(Other definitions for shadow that I've seen before include "Follow secretly; obscure" , "Follow closely - dark image - opposition" , "This opposition cabinet parallels the government" , "Sort of boxer - dog" , "Image cast - dog" .)