The rotter upset tea on a cleric! (6)

I believe the answer is:

curate

I'm a little stuck... Click here to teach me about this clue!

Here is my best explanation:

'a cleric' is the definition.
(I've seen this before)

'the rotter upset tea' is the wordplay.
'the rotter' becomes 'cur' (I can't explain this - if you can you should believe this answer much more).
'upset' indicates an anagram.
'tea' anagrammed gives 'ate'.
'cur'+'ate'='CURATE'

'on' is the link.

Can you help me to learn more?

This clue was last seen in Evening Standard