The 40% of the IRA balance that the trust inherits remains in the IRA until such time as it is distributed to the trust. Typically, the IRA distributions are limited to the RMD, but do not have to be.
Since 60% of your IRA goes elsewhere, after your death the trustee of the trust should submit your death Cert and other trust info to the IRA custodian and establish a new inherited IRA account with 40% of the balance and titled showing the trust as beneficiary of you and your DOD. It will then be determined if the trust is qualified for look through treatment or not. If qualified, the 10 year rule will apply for distribution of the IRA balance to the trust unless your niece is not more than 10 years younger than you, is still a minor, or is chronically ill or disabled. For those situations if the trust is qualified she is considered an “eligible designated beneficiary” or EDB for short, and the 10 year rule does not apply (except for minors when it kicks in at majority). If the trust is NOT qualified, perhaps because your trustee fails to provide trust documents to the IRA custodian by 10/31 of the year following your death, then the IRA must be distributed within 5 years if you pass prior to your required beginning date, OR if you pass later, then your remaining life expectancy which could be more or less than 10 years.
Therefore, your IRA still exists as an inherited IRA for the benefit of the trust until it is liquidated as required by the RMD rules or faster if the trust so indicates. This is true even though the trust will be an accumulation trust that does not have to pass RMDs out of the trust to your niece. In this situation, the trust will have to pay the taxes at the higher trust tax rates.
Note that if your trust specifies that niece is to receive RMDs only that is a problem because the 10 year rule does not have annual RMDs, so niece would get nothing until year 10, then a full lump sum. In that case, the trust should be re done.
In the most common scenario, your niece will have passed the age of majority when you pass, she will not be an EDB, and the trust will be qualified, meaning the 10 year rule applies. Just because the inherited IRA must be drained within 10 years the trust can continue and disperse funds formerly from the IRA to niece as needed or required.