The interest splits at the date of death
An inherited deposit does not change hands cleanly the moment someone dies; there is a gap while it is transmitted to your name, and the interest in that gap has to be attributed correctly. Interest credited up to the date of death is the deceased's income, reported in their final return filed by the legal representative under Section 159. Interest credited after the death is your income as the heir.
The practical snag is the PAN. Until the deposit is transmitted, the bank keeps deducting TDS on the deceased's PAN, so the credit sits against a dead person's PAN while the post-death interest actually belongs to you. That mismatch is reconciled on the returns, the deceased's final return and your own, so the TDS is not stranded. The sooner the deposits are transmitted to your name, the sooner the interest and its TDS line up under your PAN.
You cannot use the resident short-cut
A resident depositor who expects no tax files Form 15G, or Form 15H if a senior, to stop the bank deducting TDS. As an NRI heir, that door is closed: Form 15G and 15H are for residents only, and a declaration filed despite non-residence is invalid. So the resident work-around does not apply to you.
What you use instead is different and often better. Once the deposit is yours, interest for a non-resident carries TDS under Section 195, but you can cut it to the treaty rate under the double-tax agreement between India and your country, using a tax residency certificate and Form 10F, now Form 41. Where even the treaty rate over-deducts against your real tax, a lower-TDS certificate, Form 13, now Form 128, sets the bank's deduction to your actual liability. And if your PAN has gone inoperative, the TDS jumps to a flat 20%, so keeping the PAN active is worth checking first.
The deposit gets re-designated
An inherited deposit does not stay a resident deposit in your hands. When an NRI heir claims a resident fixed deposit, it is re-designated to an NRO deposit in your name, from where the balance can later be repatriated through the USD 1 million a year route. If you would rather not continue the deposit, a deceased's term deposit can be closed before maturity on inheritance and the interest for the run period is paid without the usual premature-closure penalty, and you can then re-invest as you choose.
So the sequence is: transmit the deposit, re-designate it to NRO, fix the TDS to the treaty or certificate rate, and reconcile the interest around the date of death. A practising CA runs this so the interest is taxed once, in the right hands, and the TDS is not left over-deducted on a PAN that is no longer the earner's.