The meaning of in accordance with and subject to the provisions of this act under section 4 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 High Court tried to explain the meaning of in accordance with and subject to the provisions of this act.
Meaning of in accordance with and subject to the provisions of this act defined by court
The phrase “in accordance with and subject to the provisions of this act” used in section 4 of the Income Tax Act came up before hon’ble Kerala High Court in CIT Vs. Fertilizers & Chemicals (Travancore) Ltd.  166 ITR 823 (KER.) and it explained.
Meaning: The expressions ‘in accordance with’ and ‘subject to the provisions of this act’ make it clear that the assessment of the income of a non-resident which has accrued or arisen in india through an agent, shall be subject to and in accordance with the provisions contained in chapter xv of the income-tax act.
Section 4 of Income Tax Act
Charge of income-tax.
4.(1) Where any Central Act enacts that income-tax shall be charged for any assessment year at any rate or rates, income-tax at that rate or those rates shall be charged for that year in accordance with, and subject to the provisions (including provisions for the levy of additional income-tax) of, this Act in respect of the total income of the previous year of every person :
Provided that where by virtue of any provision of this Act income-tax is to be charged in respect of the income of a period other than the previous year, income-tax shall be charged accordingly.
(2) In respect of income chargeable under sub-section (1), income-tax shall be deducted at the source or paid in advance, where it is so deductible or payable under any provision of this Act.
Updated up to Finance Act 2021