Crossword Genius

Ted missing road in my part of Kent (6)

Ross

I believe the answer is:

medway

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

'part of kent' is the definition.
(I know that Medway located in the administrative territorial entity Kent)

'ted missing road in my' is the wordplay.
I cannot really understand how this works, but
'road' could be 'way' (I've seen this in other clues) and 'way' is found within the answer.
The remaining letters 'med' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for medway that I've seen before include "River at Maidstone" , "River of Kent" .)

I've seen this clue in The Times.
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