Prime Minister initially indicates this time of day, possibly (7)
I believe the answer is:
evening
'prime minister initially indicates this time of day possibly' is the definition.
'evening' can be an answer for 'time' (time of day). I'm not certain of the rest of the definition.
'time of day possibly' is the wordplay.
'time of day' becomes 'even' (short for evening).
'possibly' becomes 'ing' (I can't explain this - if you can you should give a lot more credence to this answer).
'even'+'ing'='EVENING'
Can you help me to learn more?
(Other definitions for evening that I've seen before include "late party" , "Calming" , "Time for vespers" , "End part of the day" , "Time of falling light" .)