Posh MP in M&S makes complaint (5)
I believe the answer is:
'complaint' is the definition.
(mumps is a kind of health problem)
'posh mp in ms' is the wordplay.
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-U).
'in' means one lot of letters goes inside another.
'ump' going inside 'ms' is 'MUMPS'.
'makes' acts as a link.
(Other definitions for mumps that I've seen before include "Infectious disease, making neck glands swell" , "Viral disease mainly affecting children" , "Acute viral disease, often in children" , "Swollen-face disease" , "Disease once common in children" .)