I have unpaid PCN from my previous car. Can bailiffs take my new car?

Yes

Bailiffs can take control of goods only if they belong to the debtor.^[1]

Bailiffs cannot make searches with the DVLA or with the police to see whether a debtor has vehicles registered to their name.

You can take steps to protect your new car.^[2]

^{[1] Paragraph 10 of Schedule 12 of the Tribunals Courts and Enforcement Act 2007.
[2] Protect your car from bailiffs}