Kapur, an Indian Revenue Service officer, retired as the chairperson of the Central Board of Direct Taxes (CBDT) late last year.
She is probably the first woman to become a member of the tribunal, which hears appeals filed related to competition law.
In a communication, Compat said Kapur assumed the office of member on May 10.
The tribunal has two members apart from the chairman. The post of one member was lying vacant for quite sometime at the tribunal, which has also seen a rise in the number of appeals before it.
Compat is a statutory organisation to hear and dispose of appeals against any order passed by fair-trade regulator Competition Commission of India.