Free half of beer for a cyclist (5)
I believe the answer is:
rider
'cyclist' is the definition.
(someone riding a bike)
'free half of beer' is the wordplay.
'free' becomes 'rid' (to be free of something is to be rid of it).
'half of' suggests halving the letters.
'beer' with half the letters taken is 'er'.
'rid'+'er'='RIDER'
'for a' is the link.
(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" .)