As a millennium reminder, it'll suffice for me (4)

I believe the answer is:

dome

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'as a millennium reminder it'll' is the definition.
I can't tell whether this definition defines the answer.

'suffice for me' is the wordplay.
'suffice' becomes 'do' (synonyms).
'for' means one lot of letters go next to another.
'do'+'me'='DOME'

Can you help me to learn more?

(Other definitions for dome that I've seen before include "Old cathedral" , "Curved roof" , "Rounded roof; Greenwich tent" , "Hemispherical structure" , "Crown" .)

I've seen this clue in the Evening Standard.

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