Geese flying for cover around mid-September (5)
I believe the answer is:
skein
'geese flying' is the definition.
'cover around mid-september' is the wordplay.
'cover' becomes 'skin' (skin is a kind of cover**).
'around' is an insertion indicator.
'mid' indicates the central letters.
'september' becomes 'sep' ('Sep' can be a synonym of 'september').
The central letter of 'sep' is 'e'.
'skin' enclosing 'e' is 'SKEIN'.
'for' acts as a link.
(Other definitions for skein that I've seen before include "Loosely coiled bundle of wool" , "Loose coil of yarn" , "Ball of yarn" , "Loosely coiled length of thread" , "Birds flying" .)