Keep in mind that you can contribute to an IRA during retirement even if you've started collecting Social Security benefits. But keep in mind that what you get from Social Security doesn't qualify as earned income and therefore can't be contributed to an IRA. Yes, you can contribute to an IRA after you retire (with caveats). 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.
Contributing to an IRA or Roth IRA during retirement has benefits, depending on your particular situation. First, make sure that you actually have the taxable compensation required to make the traditional IRA or Roth IRA contributions you're considering making. However, because IRAs require earned income to make contributions, your Social Security benefits alone don't qualify you to contribute to an IRA. For contributions to a Roth IRA, make sure you can contribute to a Roth IRA right from the start.