Particular period allocated by fate (4,4)
I believe the answer is:
time slot
'particular period' is the definition.
'time slot' can be an answer for 'period' (time slot is a kind of period). I'm not sure about the 'particular' bit.
'allocated by fate' is the wordplay.
I cannot really understand how this works, but
'by' could be 'times' ('times' can mean multiplied by) and 'times' is found in the answer.
'fate' could be 'lot' (synonyms) and 'lot' is found within the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for time slot that I've seen before include "It can be scheduled" , "limited period" , "Specified interval" , "Schedule period allocated to programme" .)