The meaning of in course of proceedings under section 147 of the Income Tax Act is not defined in the act itself. But we can take guidance from decisions by various high courts. Here is an excerpt of the court’s order in which the Hon’ble High Court tried to explain the meaning of in course of proceedings.
Meaning of in course of proceedings defined by course
The phrase “in course of proceedings” used in section 147 of the Income Tax Act came up before hon’ble Kerala High Court in G. Sukesh Vs. Dy. CIT  118 TAXMAN 427/252 ITR 230 (KER.) and it explained
Meaning : The expression ‘in the course of proceedings’ is wide in its amplitude, and it will, therefore, be proper to conclude that the information at the time of issuing notice need not be complete and accurate.
Section 147 of Income Tax act
Income escaping assessment.
147. If any income chargeable to tax, in the case of an assessee, has escaped assessment for any assessment year, the Assessing Officer may, subject to the provisions of sections 148 to 153, assess or reassess such income or recompute the loss or the depreciation allowance or any other allowance or deduction for such assessment year (hereafter in this section and in sections 148 to 153 referred to as the relevant assessment year).
Explanation.—For the purpose of assessment or reassessment or recomputation under this section, the Assessing Officer may assess or reassess the income in respect of any issue, which has escaped assessment, and such issue comes to his notice subsequently in the course of the proceedings under this section, irrespective of the fact that the provisions of section 148A have not been complied with.]
Updated up to Finance Act 2021.