Part of leaf from flyer one's picked up (6)
I believe the answer is:
midrib
'part of leaf' is the definition.
(I've seen this before)
'flyer one's picked up' is the wordplay.
'flyer' becomes 'bird' ().
'one's' becomes 'I'm' ('one is' is a formal way of saying 'I am').
'picked up' says the letters should be written backwards.
'bird'+'im'='birdim'
'birdim' in reverse letter order is 'MIDRIB'.
'from' is the link.
(Other definitions for midrib that I've seen before include "Large vein on leaf" , "Central leaf vein" , "major vein" , "part of leaf" , "Part of leaflet" .)