A 401(k) is a work-sponsored plan, and you can only make contributions through the employer, you can't make private contributions.
The fact that you would be receiving a pension from a previous employer does not stop you from participating in a 401(k) offered by a new employer. If you make pre-tax contributions, you will still get that tax benefit (the amount is already removed from your W-2 taxable wages by your employer, it is not a separate tax deduction on form 1040). Your employer may also offer an after-tax (designated Roth) option. At your age, a Roth account may be a better long term option, although you may want advice from a professional retirement planner.
If you have income earned from working, you would also be permitted to contribute to a private IRA (traditional or Roth) that you can open at a bank or brokerage of your choice. Whether that is tax-deductible depends on your income and the availability of a retirement option at your workplace, and is not affected by the fact that you receive a pension from a prior employer.
What you should not do without professional advice is start taking social security, if you plan on continuing to work. That can get complicated and affect your other options.
