Yes, you can contribute to an IRA after you retire, but you'll need to have a certain amount of “earned income” to do so. Earnings from work come in the form of salaries, tips, or bonuses, so you'll likely need to have at least some type of part-time work. If your spouse continues to work and has earned income, you can set up and fund a Roth IRA for you, even if you don't work actively. This marital Roth IRA must be in your name, even if your spouse is the one making the contributions.
Your traditional IRA contributions may be tax-deductible. The deduction may be limited if you or your spouse are covered by a retirement plan at work and your income exceeds certain levels. If you are retired and your spouse has earned income, he or she can contribute to their own IRA and also make what is called a spousal contribution to your IRA. If you had a SIMPLE IRA or an SEP IRA but have retired from that job, you can still open an IRA through investment firms such as Vanguard or Fidelity.
However, you can still contribute to a Roth IRA and make cumulative contributions to a Roth or traditional IRA, regardless of your age.