Old German’s afterthought about game Welsh girl (8)

I believe the answer is:

prussian

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'old german's' is the definition.
'Prussian' can be an answer for 'german's' (Prussian is an example). I'm not sure about the 'old' bit.

'afterthought about game welsh girl' is the wordplay.
'afterthought' becomes 'ps' (as in a PS in a letter).
'about' means one lot of letters goes inside another.
'game' becomes 'RU' (rugby union).
'welsh girl' becomes 'Sian' (common Welsh name).
'ps' going around 'ru' is 'prus'.
'prus'+'sian'='PRUSSIAN'

Can you help me to learn more?

(Other definitions for prussian that I've seen before include "Relating to a former German state" , "Native of a former German kingdom" , "Ova" .)

I've seen this clue in The Times.

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