Though athletic, lose time circumnavigating storage facility (6)

I believe the answer is:

closet

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'facility' is the definition.
(closet is a kind of facility)

'though athletic lose time circumnavigating storage' is the wordplay.
'CLOSET' is hidden in amongst the letters.
However, I'm unsure how this is indicated.

Can you help me to learn more?

(Other definitions for closet that I've seen before include "Secret - cupboard" , "place to store gear" , "Compartment for clothing in the US" , "little room" , "Small cupboard or recess" .)

I've seen this clue in The Irish Times.

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