Sport: tired, endlessly (4)
I believe the answer is:
wear
'sport' is the definition.
(sport can mean to wear or display on one's person)
'tired endlessly' is the wordplay.
'tired' becomes 'weary' (similar in meaning).
'endlessly' means to remove the last letter.
'weary' with its final letter taken away is 'WEAR'.
(Other definitions for wear that I've seen before include "Carry the burden" , "Have on the body as clothes or ornaments" , "fashion" , "Northern flower" , "Clothing; degrade" .)