Throw up on tunic at the anointment (7)

I believe the answer is:

unction

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'the anointment' is the definition.
(synonyms)

'throw up on tunic' is the wordplay.
'on tunic' anagrams to 'UNCTION'.
But, I'm unsure how this is indicated.

'at' acts as a link.

Can you help me to learn more?

(Other definitions for unction that I've seen before include "An anointing; oily charm" , "Ritual anointing with oil" , "Smarm -- balm" , "Balm - oily charm" , "Salve" .)

I've seen this clue in the Sydney Morning Herald.

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