Strips and endlessly sleeps around (5)
I believe the answer is:
peels
'strips' is the definition.
(I know this)
'endlessly sleeps around' is the wordplay.
'endlessly' means to remove the last letter.
'around' says the letters should be written in reverse.
'sleeps' with its final letter taken off is 'sleep'.
'sleep' in reverse letter order is 'PEELS'.
'and' is the link.
(Other definitions for peels that I've seen before include "Removes skin, rind" , "Removes the skin from an orange" , "Strips off" .)