Can a distinguished jurist, who neither remained an Advocate nor a Judicial Officer, be appointed as a Judge of Allahabad High Court:

No, a distinguished jurist who has not been an advocate or judicial officer cannot be appointed as a High Court judge. To be eligible for appointment as a High Court judge, a person must meet one of the following criteria:

Be a citizen of India

Have at least 10 years of experience as an advocate of a High Court of India

Have at least 10 years of experience as a judicial officer in the territory of India


However same can not be said with respect to JUDGE OF SUPREME COURT.
Because a distinguished jurist who has not served as a judicial officer or advocate can be appointed as a judge of the Supreme Court of India, if the President of India so decides.
To be appointed as a Supreme Court judge, a person must meet one of the following qualifications:

Be a citizen of India

Have served as a High Court judge for at least five years

Have served as a High Court advocate for at least ten years

Be considered a distinguished jurist by the President