Crossword Genius

Fish by river: one to glide across frozen surface (6)

Ross

I believe the answer is:

skater

I'm a little stuck... Click here to teach me more about this clue!

'one to glide across frozen surface' is the definition.
I can't judge whether this definition defines the answer.

'fish by river' is the wordplay.
'fish' becomes 'skate' (skate is a kind of fish).
'by river' becomes 'r' (abbreviation for river. I am not sure about the 'by' bit.).
'skate'+'r'='SKATER'

Can you help me to learn more?

(Other definitions for skater that I've seen before include "One sliding over ice" , "Streak (anag)" , "One moving over ice" , "Ice sportsman" , "Winter sports participant" .)

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