Crossword Genius

Run and run, entering race (6)

Ross

I believe the answer is:

stream

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

This clue is a quadruple definition!!

'run' is the first definition.
(I know that stream is a type of run)

'and' is a link.

'run' is the second definition.
(streaming is a kind of running)

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

'race' is the fourth definition.
(thesaurus)

Can you help me to learn more?

(Other definitions for stream that I've seen before include "Small watercourse" , "Brook or small river" , "Flow of water on land" , "Constant flow of liquid" , "Master of a tributary" .)

I've seen this clue in The Sunday Times.
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