Supreme Court of Tasmania, Ecclesiastical Jurisdiction. (Probate Court) - Intestacy.
15105, pg 205. (Sorry, I am not familiar with Tasmanian Probate Files, hope that is sufficient for referencing and locating)
Basil Charles Douglas WALSH of Glendale, Bishopsbourne, Tasmania, Retired Cook, died 21 May 1977, intestate …
8 September 1977 Letters of Administration (as he died intestate, ie without a valid will), so the court granted the Admon to ‘the lawful daughter of the deceased’ (named and further identified by her then address).
I have refrained from typing up her name, as she may well be still living, and likely born 1930s. I can see her with her husband in the 1960s, on various electoral rolls in Tasmania (same address as on the Admon file.) This couple may well be our OP's living grandparents.
https://www.findmypast.com.au/articles/glossary-of-probate-termsAdmon - If a person died without leaving a will (intestate), someone (usually a relative) could apply to the probate court for a grant of administration, which would allow them to deal with the estate. Also called Letters of AdministrationJM