Put up for hire, being sound (6)

I believe the answer is:

higher

I'm a little stuck... Click here to teach me more about this clue!

'put up for hire being sound' is the definition.
I can't judge whether this defines the answer.

'hire being sound' is the wordplay.
'being sound' indicates a 'sounds like' (homophone) clue.
'hire' sounds like 'HIGHER'.

Can you help me to learn more?

(Other definitions for higher that I've seen before include "More lofty" , "More exalted" , "More elevated" , "Loftier" , "At greater altitude" .)

I've seen this clue in the Evening Standard.

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