Hi, GeorgeFM,

Box 4a of the W-4 form was meant for you!   Here are the instructions from the IRS website:

Enter in this step the total of your other
estimated income for the year, if any. You shouldn’t include
income from any jobs or self-employment. If you complete
Step 4(a), you likely won’t have to make estimated tax
payments for that income. If you prefer to pay estimated tax
rather than having tax on other income withheld from your
paycheck, see Form 1040-ES, Estimated Tax for Individuals.

When thinking about how much additional taxable income, you will want to include that RMD if the contributions were pre-tax, particularly if you are not withholding taxes on the distributions. Note, the withholding offered by the firm may be too low to cover the tax.  Roth IRAs are generally not included in taxable income if you waited 5 years to withdraw the earnings and you are over 59.5.  More info on that topic here. Also, don't forget to include in taxable social security.  You can get taxed on up to 85% of your social security income if your combined married filing joint income is more than $44K.  This article explains that and many folks are not aware that social security income can be taxable. 

Adjusting your W-4 is an easy option. However, you can also just pay estimated taxes. This article explains that.  The IRS doesn't care if you withhold or send in estimated taxes, just as long as they get their money.  FYI, many firms will also withhold and remit taxes on your RMD's, if you choose.  Pick the method(s) that works for you!  One very simple method to get you close, if things are pretty much the same as last year, is to look at the amount of last year's underpayment and use forms 1040-ES to send in that amount about quarterly.  Estimated taxes are generally due April 15, June 15, Sept 15 and January 15 (for the prior year).  If you want,  you can round up a bit to give you some cushion.

Since you are starting a little late this year, you may still get a small underpayment penalty. The IRS doesn't just want it's money, it wants it in the timeline it wants it!  Don't worry about that too much.  Just catch up now using the method that works best for you.