Like wild unicorn right away in Paraguay port? (8)

I believe the answer is:

asuncion

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'port?' is the definition.
(I know that Asuncion is a port)

'like wild unicorn right away in' is the wordplay.
'like' becomes 'as' ().
'wild' is an anagram indicator.
'right' becomes 'r' (common abbreviation).
'away' indicates named letters should be taken away.
'in' means one lot of letters goes inside another.
'unicorn' with 'r' removed is 'unicon'.
'unicon' anagrammed gives 'uncion'.
'as' going into 'uncion' is 'ASUNCION'.

'paraguay' acts as a link.
I am not very happy about this link. It may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for asuncion that I've seen before include "Capital of Paraquay" , "South American capital city" , "Capital city of Paraguay" .)

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

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