Fast asleep after lying down (4,3)
I believe the answer is:
flat out
This clue might be a double definition.
'fast asleep' is the first definition.
'flat-out' can be an answer for 'fast' (thesaurus). I'm not certain of the 'asleep' bit.
'lying down' is the second definition.
(laying flat on the ground)
'after' acts as a link.
Can you help me to learn more?
(Other definitions for flat out that I've seen before include "very quickly?" , "Ready to drop" , "Exhausted - at full speed" , "Lying on floor" , "full tilt?" .)