Listener is glued to The River of Death (4)

I believe the answer is:

styx

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

'river of death' is the definition.
'styx' can be an answer for 'river' (mythical river). I'm not certain of the 'of death' bit.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for styx that I've seen before include "River of hell" , "Underworld river; sounds like remote area" , "River around Hades" , "One of the underworld rivers" , "River separating Earth from Hades" .)

I've seen this clue in the Sydney Morning Herald.

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