A blur, a sleep, awfully nice (11)
I believe the answer is:
pleasurable
'nice' is the definition.
(thesaurus)
'a blur a sleep awfully' is the wordplay.
'awfully' indicates an anagram.
'a'+'blur'+'a'+'sleep'='ablurasleep'
'ablurasleep' is an anagram of 'PLEASURABLE'.
(Other definitions for pleasurable that I've seen before include "Enjoyable" , "Such as gives enjoyment" , "Delightful" .)