Sleeps up in the bridge (4)
I believe the answer is:
span
'bridge' is the definition.
(I know that bridge can be written as span)
'sleeps up' is the wordplay.
'sleeps' becomes 'naps' (napping is a kind of sleeping).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'naps' written backwards gives 'SPAN'.
'in the' acts as a link.
(Other definitions for span that I've seen before include "Stretch; traverse" , "too short for the foot" , "Extent of aircraft's wing" , "Bridge - rotated" , "Duration, length" .)