Writer on computer matters, unknown expert (9)
'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).
(Other definitions for authority that I've seen before include "Mandate", "Power, influence", "Expert; permission", "Power to expercise control".)