Crossword Genius

Get rid of priest with woman at early opener (9)

Ross

I believe the answer is:

eliminate

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

'get rid' is the definition.
(I've seen this before)

'priest with woman at early opener' is the wordplay.
I cannot really understand how this works, but
'priest' could be 'eli' (biblical figure) and 'eli' is found within the answer.
'woman' could be 'mina' and 'mina' is found in the answer.
The remaining letters 'te' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'of' is the link.

Can you help me to learn more?

(Other definitions for eliminate that I've seen before include "Annihilate" , "Murder" , "Knock out" , "Remove from contention" , "Do away with, remove" .)

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