I owe money from 2014. I paid estimates quarterly tax in 2020. Will the estimates tax be applied to my old tax debt first?

[DoninGA]

Don't think so.  Those estimated tax payments will be applied to the 2020 taxes owed.

If you are receiving a tax refund on the 2020 tax return, the IRS will seize the refund and apply it to the back taxes owed.

You can see the amount of back taxes owed on your tax account - https://www.irs.gov/payments/view-your-tax-account

You can pay the back taxes owed using the IRS payment website for Direct Pay - https://www.irs.gov/payments/direct-pay

[Critter-3]

Correct ... if you make estimates for a certain tax year they are first applied to that tax year on that year's  return and then if there is any refund on that year's return  it will be taken for any and all back taxes owed or other offsets the IRS collects for like state balance dues or child support.