Heard field bear down on breathing space (6)

I believe the answer is:

leeway

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'breathing space' is the definition.
'leeway' can be an answer for 'space' (I've seen this before). I am unsure of the 'breathing' bit.

'heard field bear down' is the wordplay.
'heard' shows a homophone (sound like).
'field' becomes 'lea' (lea can mean a meadow or field of grass).
'bear down' becomes 'way' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'lea' sounds like 'lee'.
'lee'+'way'='LEEWAY'

'on' is the link.

Can you help me to learn more?

(Other definitions for leeway that I've seen before include "Allowable margin, latitude" , "Drift - scope for action" , "Elbowroom" , "Freedom to act" , "Amount of freedom" .)

I've seen this clue in the Sydney Morning Herald.

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