If you are a W2 employee who started freelancing, do you need to pay quarterly for 1099 income that started part way through the year?

Yes, if you have self-employed income starting mid-year, you should pay estimated taxes from the quarter in which you start having self-employed income to avoid having to pay a penalty for underpayment of estimated taxes.

Please read this TurboTax article for more information.

If you prefer, you can increase the withholding from your W-2 job to cover the tax on your 1099 income, instead of making separate quarterly estimated tax payments.