Becomes liable for fashionable dogs (6)
I believe the answer is:
incurs
'becomes liable for' is the definition.
(I've seen this before)
'fashionable dogs' is the wordplay.
'fashionable' becomes 'in' ('in' can be similar in meaning to 'fashionable').
'dogs' becomes 'curs' (cur is a kind of dog).
'in'+'curs'='INCURS'
(Other definitions for incurs that I've seen before include "Brings on oneself as consequence" , "Becomes liable (to) - suffers" , "Provokes" , "Brings on oneself, maybe something unpleasant" , "Sustains" .)