Crossword Genius

Ice cream sandwiches minister ate at front (9)

Ross

I believe the answer is:

eliminate

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

'ice' is the definition.
The answer and definition can be both related to change as well as being verbs in their base form.
Maybe they are linked in a way I don't understand?

'cream sandwiches minister ate at front' is the wordplay.
'cream' becomes 'elite' (as in the cream of the crop).
'sandwiches' is an insertion indicator (goes on either side like a sandwich).
'minister' becomes 'min' (abbreviation).
'at front' says to take the initial letters.
The first letter of 'ate' is 'a'.
'min'+'a'='mina'
'elite' placed around 'mina' is 'ELIMINATE'.

Can you help me to learn more?

(Other definitions for eliminate that I've seen before include "put out" , "Remove from contention" , "Discard - exclude" , "Get rid of, or exclude from further stage of game" , "Take out" .)

I've seen this clue in The Sunday Times and The Times.
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