The deceased’s estate is valued at £370K. The full NRB is available, reducing the chargeable estate to £45K.
The RNRB cannot be claimed, but the TNRB can be claimed.
If the TNRB is claimed, there will be no IHT.
Will an IHT400 still need to be submitted to claim the TNRB? There is no need for a grant - all assets have been realised/paid to estate without any request for a grant.
It would be treated as an excepted estate, so generally no IHT 400 required if they died on or after 1 Jan 2022, subject to a few exemptions. You will see from the link below that the TNRB does need to be claimed within 2 years of death. If you prefer you could do an IHT400, but I would have thought a probate application as it is an exempt estate would probably be easier, and then they would have the probate just in case it was needed in the future. IHTM06025 - Rules about excepted estates: making a claim to transfer unused nil rate band - HMRC internal manual - GOV.UK