Period of which the present day is near the end (8)
I believe the answer is:
december
'period of which the present day is near the end' is the definition.
'December' can be an answer for 'period' (December is an example). I'm unsure of the rest of the definition.
'period of which' is the wordplay.
'period' becomes 'Dec' (Dec is an example).
'of which' becomes 'ember' (I am not sure about this - if you are sure you should believe this answer much more).
'dec'+'ember'='DECEMBER'
(Other definitions for december that I've seen before include "Last month" , "Tenth month to the old Romans" , "Winter month" , "12th month" , "Original tenth month" .)