The meaning of at the time of his retirement under section 10(10AA) of the Income Tax Act is not defined in the act itself. But we can take guidance from decisions by various high courts. Here are excerpts of courts orders in which the Hon’ble Income Tax Appellate Tribunal tried to explain the meaning of at the time of his retirement.

Meaning of at the time of his retirement defined by court
The phrase ‘at the time of his retirement’ used in section 10(10AA) of the Income Tax Act came up before hon’ble ITAT-Delhi in Col. (Retd.) Chandra Kumar Shukla v. Asstt. CIT [2007] 15 SOT 229 (Delhi – Trib.) and it explained.
Meaning : The expression ‘at the time of his retirement’ occurring in sub-clause (ii) of section 10(10aa) refers to the period of earned leave at the credit of the private employee, and not a government employee, which he might have encashed at the time of his retirement from government service.
Section 10(10AA) of the Income Tax Act
10(10AA). (i) any payment received by an employee of the Central Government or a State Government as the cash equivalent of the leave salary in respect of the period of earned leave at his credit at the time of his retirement whether on superannuation or otherwise;
(ii) any payment of the nature referred to in sub-clause (i) received by an employee, other than an employee of the Central Government or a State Government, in respect of so much of the period of earned leave at his credit at the time of his retirement whether on superannuation or otherwise as does not exceed ten months, calculated on the basis of the average salary drawn by the employee during the period of ten months immediately preceding his retirement whether on superannuation or otherwise, subject to such limit as the Central Government may, by notification in the Official Gazette, specify in this behalf having regard to the limit applicable in this behalf to the employees of that Government :
Provided that where any such payments are received by an employee from more than one employer in the same previous year, the aggregate amount exempt from income-tax under this sub-clause shall not exceed the limit so specified :
Provided further that where any such payment or payments was or were received in any one or more earlier previous years also and the whole or any part of the amount of such payment or payments was or were not included in the total income of the assessee of such previous year or years, the amount exempt from income-tax under this sub-clause shall not exceed the limit so specified, as reduced by the amount or, as the case may be, the aggregate amount not included in the total income of any such previous year or years.
Explanation.—For the purposes of sub-clause (ii),—
the entitlement to earned leave of an employee shall not exceed thirty days for every year of actual service rendered by him as an employee of the employer from whose service he has retired;
In this article, you can get guidance from high courts on the meaning of at the time of his retirement under section 10(10AA) of the Income Tax Act.
Updated up to Finance Act 2021