Stepped over to cover chap asleep (7)
I believe the answer is:
dormant
'asleep' is the definition.
(I've seen this before)
'stepped over to cover chap' is the wordplay.
'stepped' becomes 'trod' ('tread' can be a synonym of 'step').
'over' says the letters should be written in reverse.
'to cover' means one lot of letters goes inside another.
'chap' becomes 'man' (I've seen this before).
'trod' back-to-front is 'dort'.
'dort' going around 'man' is 'DORMANT'.
(Other definitions for dormant that I've seen before include "Inactive, but not dead" , "Sleeping or inactive, say volcano" , "Comatose" , "Inert" , "Lying inactive as if in sleep" .)