Criticise dog name this writer's introducing (6)
I believe the answer is:
impugn
'criticise' is the definition.
(I've seen this before)
'dog name this writer's introducing' is the wordplay.
'dog' becomes 'pug' (pug is a kind of dog).
'name' becomes 'n' (common abbreviation e.g. on forms).
'this writer's' becomes 'i'm' ('I am' referring to the writer of the clue).
'introducing' is a charade indicator (letters next to each other) (some letters go before others).
'pug'+'n'='pugn'
'pugn' put after 'im' is 'IMPUGN'.
(Other definitions for impugn that I've seen before include "Dispute honesty of (someone's motive)" , "Attack as false, challenge" , "Try to discredit, express doubts about honesty" , "Express doubts about truth or honesty of, say motives" , "Call into question or attack by words" .)