Next to calm host when starters don't appear (6)

I believe the answer is:

almost

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'next' is the definition.
Both the definition and answer are adverbs. Perhaps they are linked in a way I don't understand?

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for almost that I've seen before include "Not totally" , "Slightly short of" , "practically" , "Not entirely" , "Virtually" .)

I've seen this clue in The Times.

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