Closely examine report of newspaper delivery (7)
I believe the answer is:
eyeball
'closely examine' is the definition.
(I've seen this before)
'report of newspaper delivery' is the wordplay.
'report of' shows a homophone (sound like).
'newspaper' becomes 'i' (UK newspaper).
'delivery' becomes 'ball' (delivery in cricket).
'i' is a homophone of 'eye'.
'eye'+'ball'='EYEBALL'
(Other definitions for eyeball that I've seen before include "One of two in confrontation" , "One faces one in confrontation" , "Closely examine" , "Organ of sight" , "Socket filler" .)