Would you use "for the adaptation" in this context?
Considering the application submitted by XXX for the adaptation to the new public health regulation applicable to the animal by-products not intended for human consumption.
It doesn't seem to make sense that an "application" would be submitted for "adaptation". What do you mean by "application". Also this appears not to be a complete sentence. I would suggest that two instances of "the" be removed as follows, but I think you need to define the terms I have just mentioned in order to get a complete answer, and perhaps explain how this is a sentence, or why it doesn't need to be.
Considering the application submitted by XXX forthe adaptation to the new public health regulation applicable to the animal by-products not intended for human consumption.
Substituting request, will not turn this sentence fragment into a sentence.
It may help if you could write two or three short sentences explaining what your long sentence should mean. It is possible that adaption (meaning modification or change) should be adoption, but even then there would be other problems with the sentence. That is why MM and I are asking for clarification.