What may kept be in cupboard, second-rate space? (5)

I believe the answer is:

broom

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'what may kept be in cupboard' is the definition.
I can't judge whether this defines the answer.

'second-rate space?' is the wordplay.
'second rate' becomes 'b'.
'space?' becomes 'room' (enough space or room to do something).
'b'+'room'='BROOM'

Can you help me to learn more?

(Other definitions for broom that I've seen before include "Flowering shrub" , "cleaner" , "A new - - sweeps clean" , "Sweeper (said twice for a car!)" , "Shrub or sweeping brush" .)

I've seen this clue in The Times.

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