You can run the estate remotely
Being an executor from abroad does not mean flying back and forth. The standard route is to grant a registered power of attorney to a trusted person, often the family CA or a professional, in India, who then deals with the banks, the registrars, the housing society and the tax authorities on your behalf. A power of attorney executed abroad needs to be notarised and legalised or apostilled, and stamped in India, to be usable, which a practising CA arranges.
With that in place, the day-to-day administration, collecting the assets, paying the estate's liabilities, obtaining any grant an institution insists on, filing the estate's returns, is handled on the ground in India while you supervise from abroad. So the practical burden of being an executor is manageable remotely, provided the authority is set up correctly at the start.
The estate's income is taxed in your hands until it is distributed
This is the part most executors do not expect. Between the date of death and the point at which the estate is fully distributed to the beneficiaries, the income the estate earns, rent from a property, interest on deposits, is chargeable to tax in the hands of the executor (Section 168), assessed separately from your own personal income. If there is more than one executor, the estate is assessed as an association of persons.
There is a genuine quirk to flag. For this estate income, the residential status that applies is the deceased's status, not yours. So even though you, the executor, are an NRI, the estate income is assessed according to how the deceased was placed. Once an asset is handed to a beneficiary and its income is taxed in their hands, that income is excluded from the estate's assessment, so the estate is only ever taxed on what it still holds and has not yet passed on.
Your liability, and the eventual distribution
As executor you are a legal representative, responsible for settling the estate's and the deceased's tax, but only up to the value of the estate (Section 159). You are not personally exposed beyond what the estate is worth, which is an important reassurance when you are administering it from a distance.
When assets are eventually distributed, or sold to fund distribution, the tax follows the ordinary rules: a sale of inherited property carries the deceased's cost and holding period, and the buyer deducts TDS under Section 195 where a beneficiary or the estate is non-resident. A practising CA runs the estate's separate assessment while it is being administered, keeps the executor's own return apart from it, and closes the estate cleanly once distribution is complete.