'Commissionerate' doesn't appear in the OED Online. The sense it would convey is attested for 'commissionership' instead.
The district under the jurisdiction of a commissioner.... Now chiefly hist.
Recorded earliest in chief commissionership.
Freq. with reference to the British Empire, esp. British India.
The position, office, or term of office of a commissioner (in various senses).
["commissionership, n.". OED Online. December 2015. Oxford University Press. http://www.oed.com/view/Entry/37148?rskey=EZ6AnF&result=55&isAdvanced=false (accessed December 19, 2015).]
Examples of this use of 'commissionership' are given dating from 1625 to 2007 (Encycl. N.-E. India).
As for the correctness of 'commissionerate' or 'commissionerat', I'm not sure what 'correct' means.
- Because there are examples of the word in contemporary use, the word is in that limited way correct.
- The word will be understood with either spelling.
- Google and DuckDuckGo searches produce approximately the same number of results for 'commissionership' and 'commissionerate'.
- Other dictionaries than the OED list 'commissionership', but not 'commissionerate'.
- The '-ate' suffix is used chiefly to form
a. Substantives denoting office or function, or the persons performing it ....
- This meaning of '-ate' does not apply so readily to what I take to be your intended meaning as does the meaning of '-ship':
Added to ns. designating an official or person of rank to denote the office, position, dignity, or rank of the person designated ....
- The '-at' suffix is the original form of the '-ate' suffix with the meaning shown under (5) above. It is less likely than the '-ate' suffix to be considered correct.
All the foregoing aside, I suspect that by "office establishment" in your question, you intended "office building" or the "office suite" (where "suite" is a collection of physical offices within a building or set of buildings). In that case, the usual American English and likely the usual British English word you want is probably
where "Commission" is an abbreviation of the full title of the commission. For example, this
Commissionerate of Higher Education, Education Department - Government of Gujarat
(From the website of the Commissionerate of Higher Education, Education Department - Government of Gujarat.)
would be this
Commission of Higher Education, Education Department - Government of Gujarat
Office of the Commissioner of Higher Education is responsible for executing policy initiatives, regulating & funding higher education system of the State, in a network of universities, affiliated colleges and research institutions. ...
would be this
Office of the Commission etc.
idiomatically in American English. If "Commission" (or the full title of the commission) is not sufficient to unambiguously refer to the buildings or suite of offices housing the Commission of Higher Education,
office (or offices) of the Commission of Higher Education
would be used idiomatically.
None of the foregoing is intended to suggest that the American or British dialects of English are any more correct than other dialects of English.