The dog, the time after, got upset by the poison (6)
I believe the answer is:
curare
'the poison' is the definition.
(curare is a poisonous plant)
'the dog the time after got upset' is the wordplay.
I cannot quite see how this works, but
'dog' could be 'cur' (a cur is an aggressive or scruffy dog) and 'cur' is present in the answer.
The remaining letters 'are' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
'by' is the link.
Can you help me to learn more?
(Other definitions for curare that I've seen before include "Poison applied to darts" , "Arrow poison" , "Poison used on darts" , "Paralysing plant poison" , "Poison put on arrows" .)