Are Rabbonim in modern times allowed/capable of understanding biblical distinctions that were not previously explained in new ways using the acceptable methods of Halachic exegesis? Is it possible for there to be modern understandings of Torah She’biksav that differ from how it may have been understood in the Talmud or in Rambam?
This is a delicate question.
In principle, there is no reason why sages of today should not be able to interpret and to reinterpret pesukim of scripture in new ways, based on new understanding that was not available before, and by means of similar hermeneutical tools that were available to Chazal.
However, this is not done, and the Rambam already writes in his Introduction that after the Talmud was sealed, we no longer have the right to extract halachah from the Torah in a way other than that which Chazal present. The assumption is that we today lack the greatness of the Talmudic Sages, and therefore we can only rely on the interpretations that they already made.
It is a delicate matter because the ability to interpret or to reinterpret scripture (as was done in times of Chazal) can “open up” halachos that the Gemara establishes. For instance, somebody might suggest that based on modern understanding of gender issues, there is room to interpret different halachos pertaining to women in a different light.
This possibility can of course quickly lead to a wholesale “reform” and to empty Judaism of its content. Therefore, in additional to our smallness in relation to Chazal, our interpretation (in a halachic sense) begins from the Gemara, and halachah – even since the times of Chazal – is based primarily on the Talmud and not on new interpretations of the Torah.