Will capital gains tax lead to under payment penalty?

You need to pay estimated tax if you expect to owe tax or $1,000 or more.

There is a safe harbor, however, based upon your tax liability for the previous tax year.

See https://www.irs.gov/businesses/small-businesses-self-employed/estimated-taxes

Q. Can tax on capital gains  lead to under payment penalty?

A. Yes.

Q.  I've heard the IRS may look differently on capital gain taxes since it's not the "regular" tax I have deducted from my paychecks throughout the year. Is this true?

A. No.

What you probably heard was that due to the lower tax rates (some may be "taxed" at 0%) on long tern capital gains (LTCG), there is frequently little or no tax actually due.  But this depends on your total income. If your total income is high enough, none of your LTCG will be eligible for the 0% rate.

Try this tool https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1. Enter your regular income first to see the regular tax. Then add the LTCG to see the effect.
Enter the difference between the sale price and what you paid for it originally as Gains/Losses (long-term) (long term capital gain [LTCG]).

generally tax payments must be 1/4 of the annual requirement  due on 4/15/,6/15,9/15 and then 1/15 of following year.

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withholding is assumed to be 25% of the annual amount for each quarter but if you complete form 2210 you can use actual amount for each quarter. estimates don't work that way. they are deemed paid for the quarter in which they are timely paid. so it would be possible to have penalties for the first 3 quarters. 

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if you are subject to penalties, you can use the annualized income method to see if that would reduce your penalties. it's a pain becuase you must determine income and deductions for January thru March, January thru May, and Jan through August. the 2023 full year amount is per the actual return.

you may want to review the AI method which is on page 3 of the 2210.

https://www.irs.gov/pub/irs-pdf/f2210.pdf