Picked up stick or doorpost (4)
I believe the answer is:
jamb
'doorpost' is the definition.
(I've seen this before)
'picked up stick' is the wordplay.
'picked up' indicates a 'sounds like' (homophone) clue.
'stick' becomes 'jam' (I've seen this in other clues).
'jam' is a homophone of 'JAMB'.
'or' is the link.
(Other definitions for jamb that I've seen before include "Door sidepiece" , "Part of door frame" , "Vertical member of door frame" , "Door, window side post" , "Vertical side of a doorway" .)