Happy looks having covered initial distance (5)
I believe the answer is:
miles
'distance' is the definition.
(I've seen this in another clue)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for miles that I've seen before include "'But I have promises to keep, and . . . . . to go before I sleep' (Frost)" , "Imperial units of length" , "a long way" , "Distance units" .)