I'm retired but recently started a small contracting job. I get paid hourly, not an employee, and only a few hours per month. Do I still need to file quarterly estimates?

If you are only working a few hours per week you may not need to file quarterly estimated payments. 

https://ttlc.intuit.com/questions/1901110-do-i-need-to-make-estimated-tax-payments-to-the-irs

But you will end up paying self-employment tax for Social Security and Medicare even if you are retired from your former career.     No matter how old you are---if you earn income from working you will still have to pay in to SS and Medicare.

https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/26653

https://ttlc.intuit.com/community/self-employed/help/what-is-the-self-employment-tax/00/25922

https://ttlc.intuit.com/questions/2902389-why-am-i-paying-self-employment-tax

https://ttlc.intuit.com/questions/1901340-where-do-i-enter-schedule-c

https://ttlc.intuit.com/questions/3398950-what-self-employed-expenses-can-i-deduct

First off be happy --

enjoy you are working because you want to -

enjoy the fact that your are building more Social Security Credits -yes by paying in with the self-employment tax 

As long as you paid the IRS - in 2023 what your tax liability was in 2022 -- I believe you should be fine.

My rule is - if your getting a 1099 put 33% of the gross away -- each time you receive a check - it's fun after you do your taxes you may have left overs --- to do what ever you want with!

Happy Spring!