Northeast part of Athens, mainly inhabited, by the Welsh (5)

I believe the answer is:

neath

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'the welsh' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'northeast part of athens mainly inhabited' is the wordplay.
'northeast' becomes 'NE' (abbreviation).
'part of' suggests taking the first letters (I've seen 'part' mean this).
'mainly inhabited' becomes 'th' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The first letter of 'athens' is 'a'.
'ne'+'a'+'th'='NEATH'

'by' acts as a link.

Can you help me to learn more?

(Other definitions for neath that I've seen before include "town in South Wales" , "Welsh rugby club" , "not on top" , "River" , "Lower than - a town in West Glamorgan" .)

I've seen this clue in the Evening Standard.

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