Crossword Genius

Eminent politician, say, cutting shrubs on island (5,9)

Ross

I believe the answer is:

elder statesman

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'island' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.

'eminent politician say cutting shrubs on' is the wordplay.
'eminent politician' becomes 'statesman' (I've seen this before).
'say' becomes 'eg' (both can mean 'for example').
'cutting' means to remove the last letter.
'shrubs' becomes 'lder' (I can't explain this - if you can you should believe this answer much more).
'on' means one lot of letters go next to another.
'eg' with its last letter taken off is 'e'.
'e'+'lder'='elder'
'statesman' put after 'elder' is 'ELDER STATESMAN'.

Can you help me to learn more?

(Other definitions for elder statesman that I've seen before include "Experienced politician" , "John Major?" , "member with gravitas" , "Perhaps Clinton" , "veteran politician - with 17d" .)

I've seen this clue in The Times.
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