Old boy cut round rare newspaper (8)
I believe the answer is:
observer
'newspaper' is the definition.
(I know this)
'old boy cut round rare' is the wordplay.
'old boy' becomes 'OB' (abbreviation for a private school 'old boy').
'cut' becomes 'sever' (severing is a kind of cutting).
'round' indicates putting letters inside.
'rare' becomes 'r' (listed by Oxford Dictionary of Abbreviations).
'sever' placed around 'r' is 'server'.
'ob'+'server'='OBSERVER'
(Other definitions for observer that I've seen before include "One keeping his eye on" , "Viewer" , "Newspaper - witness" , "Someone watching" , "Looker-on" .)