As far as I know, you are not permitted to defer severance pay to a 401(k).
I assume that you are asking about making a 2024 IRA contribution since presumably you would have received enough regular compensation in 2023 to support a 2023 IRA contribution. If you are age 50 or over in 2024 and your 2024 Form W-2 shows at least $7,500 in box 1, you can contribute $7,500 to a traditional IRA for 2024. Depending on your modified AGI for the purpose, you might be eligible to contribute to a Roth IRA instead. Whether a traditional IRA contribution will be deductible will depend on your modified AGI for the purpose and whether you are covered by a workplace retirement plan for the year of the contribution. Even if you left the employer before 2024, you might still be covered for 2024 depending on whether the plan uses a fiscal tax year or a calendar tax year.
