Let's assume that in a head-final language like Turkic ones In complement clauses embedded clause is a TP, the verb occupies T position and the subject Spec-TP. Let's also assume that we have an evidence that over the complement clause there is an NP and Dp. For certain reasons the subject moves from spec-TP to Spec-DP( for Gen case). Is it possible that verb also moves from T to N or D for specific reasons or is it absurd to think that verbal element moves to nominal head?
Your question seems to presuppose the framework of minimalist syntax as it has been practiced in the last 20 years, so my answer is in this framework as well.
In this framework, categories like N, D and T are not primitive but should rather be considered as convenient placeholders for common configurations of syntactic features. Now a tension inevitably appears: either you define T (and the rest) by such a specific configuration, or you choose to call T the syntactic object that actually occurs in your language of study closest to the usual configuration. Under the first choice, then the answer of your question depends on your definition of N and T, but usual choices will preclude the movement you imagine (N is not supposed to be able to probe, and even if were, it is unclear to me what it could possibly probe in T). If you go the second route, then it all depends on your choice of language and like curiousdannii, I'd be interested in specific examples.
Now, based on the few hints that you provide, I imagine that you are interested in genitive subjects in relative clause in Turkic languages. I base my answer on the case of Turkish, which is the only situation I understand (even to a limited extent). In that case, you can notice that the verb exhibits a nominalizing suffix before the agreement morpheme, so that the most straightforward explanation is head movement of V to a defective T (pseudo-nominalization) followed by movement of the subject to spec TP followed by an Agree operation with a nominal C for purpose of genitive Case assignment. This last Agree operation is typically not accompanied by movement as far as I can tell. This accounts is theoretically very different from the head movement you suggest but I will note that pseudo-nominalization followed by raising of the subject and Agree with a nominal C looks superficially very much like head movement of T to N, so perhaps this is indeed what you had in mind. If this is indeed what you had in mind, the way to tease out the two accounts is adverb placements: if T moves, then the subject should be able to surface to the right of T-adverbs; if the subject moves then agrees, it should be to the left of T-adverbs. Again, an example could help (and the works of Kornfilt seem to be a good reference).