Assuming that $P \neq NP$, show that there exist sets $A$ and $B$ in $NP$ such that neither $A \leq _T^p B$ nor $B \leq _T^p A$
There is a well-known classical result of the theory of $p$-degrees stating that every non-zero $p$-T-degree splits into two incomparable $p$-T-degrees.

So assuming $P\neq NP$, by the splitting theorem, the $p$-T-degree of Turing-complete problem for $NP$ splits into two non-T-complete incomparable $p$-T-degrees.

REFERENCES

Sublattices of the polynomial time degrees

LADNER, R. E. (1973), Polynomial time reducibility, in Proc. 5th Annual ACM Sympos. on Theory of Comput., pp. 122-129

LADNER, R. E. (1975), On the structure of polynomial time reducibility, J. Assoc. Comput. Math. 22, 155-171