Adrian regularly observed writer's language (6)
I believe the answer is:
arabic
'language' is the definition.
(Arabic is a language)
'adrian regularly observed writer's' is the wordplay.
'regularly observed' indicates alternate letters (letters selected at regular intervals).
'writer' becomes 'bic' (kind of pen).
The alternating letters of 'adrian' are 'ara'.
'ara'+'bic'='ARABIC'
(Other definitions for arabic that I've seen before include "Middle Eastern language" , "Correspond; last word of Othello" , "Official language of Egypt" , "Language (by gum!)" , "connected with gum" .)