Unusually, hesitates to take away the rest (6)
I believe the answer is:
siesta
'rest' is the definition.
(I know that siesta is a type of nap)
'unusually hesitates to take away the' is the wordplay.
'unusually' is an anagram indicator.
'to take away' suggests deleting specific letters.
'hesitates' with 'the' removed is 'siates'.
'siates' is an anagram of 'SIESTA'.
(Other definitions for siesta that I've seen before include "After lunch nap" , "Afternoon snooze" , "Forty winks" , "Diurnal nap in Spain" , "Early afternoon nap" .)