Piece of fur gentlewoman's pressing (6)
I believe the answer is:
urgent
'pressing' is the definition.
('urgent' can be a synonym of 'pressing')
'piece of fur gentlewoman's' is the wordplay.
'piece of' indicates the answer is hidden within the clue.
'URGENT' is hidden in the letters of 'fur gentlewoman'.
(Other definitions for urgent that I've seen before include "Requiring immediate attention" , "To be done asap" , "Needing early action" , "demanding speedy action" , "Calling for immediate attention" .)