Yes, you would typically apply for the EIN for the estate, if you have been designated as the executor or personal representation.
Here are the basic duties:
The primary duties of a personal representative are to collect all the decedent's assets, pay his or her creditors, and distribute the remaining assets to the heirs or other beneficiaries.
The personal representative also must perform the following duties.
Apply for an employer identification number (EIN) for the estate.
File all income tax
returns and the estate tax
return when due.
Pay the tax determined up to the date of discharge from duties.
Other duties of the personal representative in federal tax
matters are discussed in other sections of this publication. If any beneficiary is a nonresident alien, see Publication 515, Withholding
of Tax on Nonresident Aliens and Foreign Entities, for information on the personal representative's duties as a withholding agent.