Almost relaxed, accepting constant postponement (7)
I believe the answer is:
respite
'postponement' is the definition.
(thesaurus)
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for respite that I've seen before include "Pause; reprieve" , "Relaxation" , "Pause from exertion, etc" , "Pause from pain" , "Relief; breather" .)