Unless you have opened your sibling's estate by (1) having her Will admitted to probate and you appointed as an Executor, or (2) applying for Letters of Administration and getting appointed as the administrator of her estate, then you have no standing to apply for any taxpayer identification number for her estate (which is actually known as an "employer identification number" or "EIN"). So, if you haven't taken care of that first, don't even try to apply for an EIN for the estate.
If you HAVE gotten appointed as the Executor or administrator of the estate, and have your Letters Testamentary or Letters of Administration, then you can obtain an EIN for the estate online using the following link: https://www.irs.gov/businesses/small-businesses-self-employed/apply-for-an-employer-identification-number-ein-online
If you have an attorney helping you with the estate administration (and if you don't, please reconsider that decision and hire a good probate attorney as soon as possible), it may be best if the attorney obtains the EIN for you. If you insist on doing things yourself, please note: There is NO CHARGE for an EIN from the IRS. If you find yourself being asked to pay for the EIN during the online application process, get the heck away from that website immediately. Unfortunately, there are "services" out there that basically have you fill out the EIN application through their filter, and then charge you for the privilege. These are scams. The IRS does not charge you for an EIN.
Best wishes to you.
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