It appears he died on 30 June 2021 in Johannesburg.
Although DPB2019 gives his address in Harare, Zimbabwe, given his only son lives in South Africa I thought it likely he may have moved to SA especially given his age and the situation in Zimbabwe.
The South African Govt Gazette for 10 Dec 2021 45606 p 101 gives the details of the estate:
030166/2021— (2) Mills, Peter Frederick Leighton, 1924-07-09, 2407095054180; (3) 2021-06-30,
Johannesburg; (4) --; (5) DH Hall (Agent for Executor), 17 Westminster Drive, Craighall Park 2196; (6)
His only son Michael Victor Leighton MILLS has succeeded as 4th Baronet subject to proving his claim and being entered on the Official Roll. He was born 30 Aug 1957 and m 1981 Susan DOIG apparently without issue. He is (or was) resident in Gauteng, SA. The baronetcy appears to be without heirs.
Sir Peter was the third oldest baronet. The third oldest baronet is now Sir Benjamin Brodie, 5th Baronet b 29 May 1925