Floral part of short Persian cover possibly left (6)
I believe the answer is:
carpel
'floral part' is the definition.
(organ of a flower)
'short persian cover possibly left' is the wordplay.
'short' means to remove the last letter.
'persian cover possibly' becomes 'carpet' (as in a Persian carpet).
'left' becomes 'l' (common abbreviation).
'carpet' with its final letter removed is 'carpe'.
'carpe'+'l'='CARPEL'
'of' is the link.
(Other definitions for carpel that I've seen before include "Part of a flower" , "bit of a flower" , "organ" .)