Prohibit giving publicity to old writer (9)
I believe the answer is:
proscribe
'prohibit' is the definition.
(I know that prohibit can be written as proscribe)
'giving publicity to old writer' is the wordplay.
'giving' means one lot of letters go next to another.
'publicity' becomes 'pr' (abbreviation for public relations).
'to old' becomes 'o' (common abbreviation eg in OE for Old English).
'writer' becomes 'scribe' (scribe is a kind of writer).
'pr' next to 'o' is 'pro'.
'pro'+'scribe'='PROSCRIBE'
(Other definitions for proscribe that I've seen before include "Denounce" , "Forbid; condemn" , "Prohibit" , "Ban" , "Exile" .)