Lady Muck initially rich as one's poor (11)
I believe the answer is:
marchioness
'lady' is the definition.
(marchioness is a kind of lady)
'muck initially rich as one's poor' is the wordplay.
'initially' indicates taking the first letters.
'poor' indicates anagramming the letters.
The initial letter of 'muck' is 'm'.
'rich'+'as'+'ones'='richasones'
'richasones' is an anagram of 'archioness'.
'm'+'archioness'='MARCHIONESS'
(Other definitions for marchioness that I've seen before include "Aristocratic lady" , "Noblewoman" , "noble wife, perhaps" , "Noble lady" , "Wife of a marquis" .)