Elderly claiming German that's regularly avoided tax caused annoyance (10)

I believe the answer is:

aggravated

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'caused annoyance' is the definition.
Although both the answer and definition are past participle verbs, I can't understand how they can define each other.

'elderly claiming german that's regularly avoided tax' is the wordplay.
'elderly' becomes 'aged' (synonyms).
'claiming' is an insertion indicator.
'that's regularly avoided' means one should take alternating letters (letters removed at regular intervals).
'tax' becomes 'VAT' (UK Value Added Tax).
The alternate letters of 'german' are 'gra'.
'gra'+'vat'='gravat'
'aged' going around 'gravat' is 'AGGRAVATED'.

Can you help me to learn more?

(Other definitions for aggravated that I've seen before include "made more severe" , "Made worse" , "Worsened" , "Made (offence) more serious (legal)" , "Annoyed" .)

I've seen this clue in The Telegraph.

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