I quit my old job in October and left the US in December 2018. I started a new job abroad in January 2019. In which tax year can I claim my moving expenses ?

[KarenJ]

Unfortunately, the moving expense deduction is no longer available in tax years 2018 – 2025 due to the Tax Cuts and Jobs Act (TCJA) that Congress signed into law on December 22, 2017.

https://ttlc.intuit.com/replies/3302201

[hermann-betty]

TurboTax' Help is confusing: "If you’re an active-duty service member who relocated due to a permanent change of station (PCS), your move automatically qualifies. If not, your move will need to meet certain requirements.
To qualify for this deduction as a full-time employee, you'll need to work at the new location for at least 39 weeks in the 12-month period, once you've arrived in your new city. …."

[KarenJ]

If you are not active duty military, you can, unfortunately, no longer claim moving expenses due to the changes in the tax law.