Twigs picked up from river (4)
I believe the answer is:
styx
'river' is the definition.
(mythical river)
'twigs picked up' is the wordplay.
'twigs' becomes 'sticks' (I've seen this before).
'picked up' shows a homophone (sound like).
'sticks' sounds like 'STYX'.
'from' acts as a link.
(Other definitions for styx that I've seen before include "The last river one crosses" , "Infernal runner" , "River surrounding Hades" , "River crossed at death" , "One of the underworld rivers" .)