Criticise dog name this writer's introducing (6)
I believe the answer is:
'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).
'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" .)