Old chess player dumps Charlie for Rod (6)
I believe the answer is:
fisher
'rod' is the definition.
(rod can mean someone who fishes)
'old chess player dumps charlie' is the wordplay.
'old chess player' becomes 'fischer' (chess player Bobby Fischer).
'dumps' indicates named letters should be taken away.
'charlie' becomes 'c' (phonetic alphabet: alpha, bravo, charlie etc.).
'fischer' with 'c' taken out is 'FISHER'.
'for' acts as a link.
(Other definitions for fisher that I've seen before include "Marten; angler" , "One who angles" , "Jeremy - (Beatrix Potter)" , "UK shipping forecast area" .)