Yes, if you file a supplemental or amended estate tax return and want an updated Estate Tax Closing Letter (ETCL), you must pay another user fee. According to the IRS FAQ, a separate request and an additional user fee are required to obtain an ETCL when a supplemental or amended return is filed. The user fee for requesting an ETCL is $67, and this fee applies to each request made, regardless of whether an ETCL was previously issued for the same estate.
Sources:
§ 6018. Estate tax returns
Instructions for Form 706 (09/2023)