Chef covering up hot item used for kitchen storage (3,4)

I believe the answer is:

cup hook

'item used for kitchen storage' is the definition.
(hook for storing a cup)

'chef covering up hot' is the wordplay.
'chef' becomes 'cook' (I've seen this before).
'covering' indicates putting letters inside.
'hot' becomes 'h' (abbreviation eg on taps).
'up'+'h'='uph'
'cook' enclosing 'uph' is 'CUP HOOK'.

I've seen this clue in The Guardian.

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