Rests up on bridge (4)
I believe the answer is:
span
'bridge' is the definition.
(I know that bridge can be written as span)
'rests up' is the wordplay.
'rests' becomes 'naps' (I've seen this in another clue).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'naps' in reverse letter order is 'SPAN'.
'on' acts as a link.
(Other definitions for span that I've seen before include "Distance between two points in time or place" , "The total spread" , "Section of bridge" , "Pair of horses" , "Stretch < fresh" .)