That letter, fourth time rejected, rubbished society magazine (3,6)
I believe the answer is:
the tatler
'that letter fourth' is the definition.
I know nothing about this answer so I can't tell whether this works.
'time rejected rubbished society magazine' is the wordplay.
'time' becomes 't' (abbreviation).
'rejected' is a reversal indicator.
'rubbished' becomes 'eh' (I can't justify this - if you can you should give a lot more credence to this answer).
'society magazine' becomes 'tatler ' (I've seen this before).
'eh' written backwards gives 'he'.
't'+'he'+'tatler'='THE TATLER'
Can you help me to learn more?
(Other definitions for the tatler that I've seen before include "publication" , "monthly" .)