Sweat terribly wrapping hospital bandage (6)
I believe the answer is:
swathe
'bandage' is the definition.
(swathe is a kind of bandage)
'sweat terribly wrapping hospital' is the wordplay.
'terribly' is an anagram indicator.
'wrapping' means one lot of letters goes inside another.
'hospital' becomes 'h'.
'sweat' is an anagram of 'swate'.
'swate' placed around 'h' is 'SWATHE'.
(Other definitions for swathe that I've seen before include "Bandage completely - band of mown grass" , "Broad strip or area of something" , "A broad strip as of cut grass" , "An enveloping bandage" , "Wrap in several layers" .)