At home, dog, small, suffers (6)
I believe the answer is:
incurs
'suffers' is the definition.
'at home dog small' is the wordplay.
'at home' becomes 'in' (similar in meaning).
'dog' becomes 'cur' (cur is a kind of dog).
'small' becomes 's' (abbreviation - e.g. clothes size).
'in'+'cur'+'s'='INCURS'
(Other definitions for incurs that I've seen before include "Becomes liable (to) - suffers" , "Becomes subject to" , "Provokes" , "Brings on oneself as consequence" , "Brings on oneself, maybe something unpleasant" .)