Old-style language in new daily's newspaper's leader (6)
I believe the answer is:
lydian
'old-style language' is the definition.
(historical Anatolian language)
'new daily's newspaper's leader' is the wordplay.
'new' indicates an anagram.
'leader' suggests taking the first letters.
The initial letter of 'newspapers' is 'n'.
'daily' anagrammed gives 'lydia'.
'lydia'+'n'='LYDIAN'
'in' is the link.
(Other definitions for lydian that I've seen before include "of old people" , "Subject of Croesus; a musical mode" , "ancient language" .)