Taro from the east? That’s not right for cereal plant (3)

I believe the answer is:
oat
'cereal plant' is the definition.
(oats are cereal plants)
'taro from the east? that's not right' is the wordplay.
'taro from the east?' becomes 'oa' (I can't explain this - if you can you should give a lot more credence to this answer).
'that's' is a charade indicator (letters next to each other).
'right' suggests the final letters (the letter on the right of the word).
The last letter of 'not' is 't'.
'oa'+'t'='OAT'
'for' is the link.
Can you help me to learn more?
(Other definitions for oat that I've seen before include "Cereal grass" , "Food grain" , "Basis of porridge" , "Cereal (singular)" , "Cereal plant" .)
