At end of day, covering sign of tiredness (7)
I believe the answer is:
yawning
'sign of tiredness' is the definition.
(yawning may indicate someone is tired)
'at end of day covering' is the wordplay.
'at end of' suggests the final letters.
'covering' becomes 'awning' (awning is a kind of covering).
The last letter of 'day' is 'y'.
'y'+'awning'='YAWNING'
(Other definitions for yawning that I've seen before include "Not apparently interested" , "showing sign of tiredness?" , "Bored" , "showing sign of fatigue?" , "Drowsy" .)