Quickly encompassing end of life — euphemism for “dead” (2,5)
I believe the answer is:
at peace
'euphemism for dead' is the definition.
(at peace means deceased)
'quickly encompassing end of life' is the wordplay.
'quickly' becomes 'at pace' (to do something at pace is to do it quickly).
'encompassing' is an insertion indicator.
'end of' says to take the final letters.
The last letter of 'life' is 'e'.
'atpace' placed around 'e' is 'AT PEACE'.
(Other definitions for at peace that I've seen before include "Free from distress" , "no longer with us" , "Not disputing" , "Dead?" , "pushing up the daisies" .)