Member in centre shortly producing lament (5)

I believe the answer is:

elegy

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'lament' is the definition.
(I know that lament can be written as elegy)

I don't understand the remainder of the clue.

(Other definitions for elegy that I've seen before include "Song of lamentation" , "Poetic lament for the dead" , "lines of regret" , "Mournful song or poem" , "Poem lamenting the dead" .)

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

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