Sleeps on way north, being cross (4)
I believe the answer is:
span
'being cross' is the definition.
(span can mean to cross or bridge)
'sleeps on way north' is the wordplay.
'sleeps' becomes 'naps' (napping is a kind of sleeping).
'on way north' says the letters should be written in reverse (in a down clue, letters go up or 'north').
'naps' reversed gives 'SPAN'.
(Other definitions for span that I've seen before include "Extent of bridge or life" , "Duration, length" , "Bridge or range" , "Cover" , "Section of bridge" .)