How to Say "inveterate" in Spanish
The Spanish word for “inveterate” is “crónico” — B2 level.

Examples
No le creas nada, es un mentiroso crónico.
Don't believe him at all; he's a chronic liar.
El desempleo crónico es un gran desafío para el gobierno.
Chronic unemployment is a major challenge for the government.
Hay una falta crónica de inversión en el sistema educativo.
There is a chronic lack of investment in the education system.
Using as a Noun
Sometimes you can put 'un' or 'una' before it to talk about a person, like 'un crónico' (a chronic patient), though it is more polite to say 'un enfermo crónico'.
Don't confuse with 'Crónica'
Mistake: “Using 'crónica' to mean chronic (adjective) when you actually mean 'a news report'.”
Correction: While 'crónica' is the feminine form of the adjective, as a noun 'la crónica' means a news chronicle or report.
Related Translations
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