Newspaper facing doom for a limited period (4,4)
I believe the answer is:
time slot
'a limited period' is the definition.
(I've seen this before)
'newspaper facing doom' is the wordplay.
'newspaper' becomes 'times' (The Times is an example).
'facing' is a charade indicator (letters next to each other).
'doom' becomes 'lot' (both can mean someone's fate or destiny).
'times'+'lot'='TIME SLOT'
'for' is the link.
(Other definitions for time slot that I've seen before include "Specified interval" , "It can be scheduled" , "Schedule period allocated to programme" , "limited period" .)