CMAT exam is conducted by Govt. of India appointed NTA(National Testing Agency).Normally Registration process starts in second half of December and exam is conducted in the last week of January.
But due to covid 19, last year this process was delayed! But this year, it should be on time as IIFT (other MBA entrance exam conducted by NTA) was conducted on time except some cyclone effected centres of W.Bengal, Orissa, Andhra Pradesh.
so, this year exam should be conducted on time(January last week- February first week and so you can expect beginning of registration process anytime from December 2021 -second half.
Hope, it helps.