Brightness appearing as clouds started to disperse at intervals (6)

I believe the answer is:

lustre

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'brightness' is the definition.
(lustre is a kind of brightness)

I cannot understand how the rest of the clue works.

(Other definitions for lustre that I've seen before include "Gloss - type of pottery" , "Sheen - glaze" , "Brilliancy" , "effect of reflected light" , "Distinction < in five years" .)

I've seen this clue in The Telegraph.

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