Show not taking a minute for star (3,5)

I believe the answer is:

red dwarf

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'for star' is the definition.
(red dwarf is a kind of star)

I don't understand how the rest of the clue works.

(Other definitions for red dwarf that I've seen before include "Small old cooling star" , "Small, cool star - TV show" , "Old cool star" .)

I've seen this clue in The Times.

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