Writer on computer matters, unknown expert (9)
I believe the answer is:
authority
'expert' is the definition.
(authority is a kind of expert)
'writer on computer matters unknown' is the wordplay.
'writer' becomes 'author' (synonyms).
'on' is a charade indicator (letters next to each other).
'computer matters' becomes 'it' (abbreviation for Information Technology).
'unknown' becomes 'y' (algebra).
'author'+'it'+'y'='AUTHORITY'
(Other definitions for authority that I've seen before include "Power to expercise control" , "Expert; permission" , "Mandate" , "Power, influence" .)