Crossword Genius

Free half of beer for a cyclist (5)

Ross

I believe the answer is:

rider

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'a cyclist' is the definition.
The definition and answer can be both people as well as being singular nouns.
Maybe they are linked in a way I don't understand?

'free half of beer' is the wordplay.
'free' becomes 'rid' (similar in meaning).
'half of' suggests halving the letters.
'beer' cut in half is 'er'.
'rid'+'er'='RIDER'

'for' acts as a link.

Can you help me to learn more?

(Other definitions for rider that I've seen before include "Clause appended to a legislative bill" , "recommendation for mercy?" , "Condition - under which a horse races" , "One on horse or bike" , "recommendation made in court" .)

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