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Batting well, having right means to combat hay fever? (7)

Ross

I believe the answer is:

inhaler

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'to combat hay fever?' is the definition.
I can't tell whether this definition defines the answer.

'batting well having right' is the wordplay.
'batting' becomes 'in' (cricket term).
'well' becomes 'hale' (I've seen this before).
'having' means one lot of letters go next to another.
'right' becomes 'r' (abbreviation).
'in'+'hale'+'r'='INHALER'

'means' acts as a link.

Can you help me to learn more?

(Other definitions for inhaler that I've seen before include "Medical aid" , "Device for breathing in drug dose" , "chest expander?" , "way of taking drugs" , "Device for, eg, asthma sufferer" .)

I've seen this clue in The Independent.
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