Some tabloids principally have control over breaking news (4,5)
I believe the answer is:
stop press
'breaking news' is the definition.
'stop press' can be an answer for 'news' (I have seen 'Late news' mean 'stop press' so perhaps 'news' could also mean 'stop press'). I'm not sure about the 'breaking' bit.
'some tabloids principally have control' is the wordplay.
'principally' suggests taking the first letters.
'have control' becomes 'oppress' (I am not sure about this - if you are sure you should believe this answer much more).
The first letters of 'some tabloids' is 'st'.
'st'+'oppress'='STOP-PRESS'
'over' acts as a link.
Can you help me to learn more?
(Other definitions for stop press that I've seen before include "The way to be tyrannical" , "Latest news" , "Late news item" , "Hold the front page!" , "Late news item(s)" .)