Rings round newspaper proprietors at first for correspondents (3,4)
I believe the answer is:
pen pals
'correspondents' is the definition.
(pen pal is a kind of correspondent)
'rings round newspaper proprietors at first' is the wordplay.
'rings' becomes 'peals' (pealing is a kind of ringing**).
'round' means one lot of letters goes inside another.
'at first' suggests taking the first letters.
The initial letters of 'newspaper proprietors' is 'np'.
'peals' placed around 'np' is 'PEN PALS'.
'for' is the link.
(Other definitions for pen pals that I've seen before include "Young correspondents" , "Friends who communicate in writing" , "They correspond" , "'Friends through correspondence (3,4)'" .)