It flows through city — Newcastle (4)

I believe the answer is:

tyne

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'it flows' is the definition.
The definition suggests a singular noun which matches the answer.

'through city newcastle' is the wordplay.
'through' indicates the answer is hidden within the clue.
'TYNE' is hidden in the letters of 'city newcastle'.

Can you help me to learn more?

(Other definitions for tyne that I've seen before include "River of northeast England" , "Gateshead's river" , "River running through Newcastle" , "North of England river" , "River of Northumberland" .)

I've seen this clue in The Times.

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