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. Yes, you can contribute to an IRA after you retire (with caveats). For contributions to a Roth IRA, make sure you can contribute to a Roth IRA right from the start. Contributing to an IRA or Roth IRA during retirement has benefits, depending on your particular situation.
However, you can still contribute to a Roth IRA and make cumulative contributions to a Roth or traditional IRA, regardless of your age. First, make sure that you actually have the taxable compensation required to make the traditional IRA or Roth IRA contributions you're considering making.