Eccentric little woman bringing spice (6)
I believe the answer is:
nutmeg
'spice' is the definition.
(nutmeg is a kind of spice)
'eccentric little woman' is the wordplay.
'eccentric' becomes 'nut' (nut is a kind of eccentric).
'little woman' becomes 'meg' (character in the novel Little Women).
'nut'+'meg'='NUTMEG'
'bringing' acts as a link.
(Other definitions for nutmeg that I've seen before include "Kick the football between an opponent's legs" , "Spice for grating" , "Aromatic seed - met gnu (anag)" , "Aromatic seed for grating" , "Give out light" .)