I avow it’s a southern river! (5)

I believe the answer is:

swear

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

'i avow' is the definition.
I can't tell whether this definition defines the answer.

'a southern river' is the wordplay.
'a southern' becomes 's' (abbreviation).
'river' becomes 'wear' (I've seen this before).
's'+'wear'='SWEAR'

'it's' acts as a link.

Can you help me to learn more?

(Other definitions for swear that I've seen before include "Affirm" , "Avow" , "Express annoyance" , "Assert" , "Use indecent or blasphemous language" .)

I've seen this clue in the Evening Standard.

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