Compat, which hears appeals against rulings of fair trade regulator Competition Commission of India (CCI), comes under the Corporate Affairs Ministry.
The posts of Compat's two members have been vacant since August 2014 when Rahul Sarin had retired. Prior to that, another member Parvin Tripathi superannuated in May 2014.
While former Commerce Secretary Rajeev Kher was appointed to one of the posts in October last year, the other post remained vacant.
The applicant is required to have a professional experience of at least 25 years in competition matters, among others.
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The member would have a tenure of five years from the date of appointment or till reaching the age of 65 years, whichever is earlier, as per the circular.
The last date for submitting application is March 7, 2015.
At present, Justice G S Singhvi is the chairman of Compat. Besides the chairman, the tribunal has two members.
In recent times, many CCI rulings have been challenged by the concerned parties at the tribunal.