Fish worn out a bit swimming around river (7,5)

I believe the answer is:

rainbow trout

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

'river' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.

'fish worn out a bit swimming' is the wordplay.
'fish' becomes 'ra' (I can't explain this - if you can you should give a lot more credence to this answer).
'swimming' indicates an anagram (letters swim around into a new order).
'worn'+'out'+'bit'='wornoutbit'
'wornoutbit' with letters rearranged gives 'inbowtrout'.
'ra'+'inbowtrout'='RAINBOW-TROUT'

'around' is the link.

Can you help me to learn more?

(Other definitions for rainbow trout that I've seen before include "Popular food fish" , "game swimmer" , "Finely coloured fish" .)

I've seen this clue in The Telegraph.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.