If a decision problem $A \in \text{NP}$ and there exists reduction so that $A \leq_p B$, for decision problem B, what can be deduced about B?
$B$ cannot be the language $\emptyset$ or the language $\Sigma^*$.  Apart from that, you can conclude absolutely nothing about $B$.

So, the given condition doesn't rule out anything useful about $B$; just about everything remains possible.  $B$ could be in $P$, or it could be in $NP$, it could be harder than anything in $NP$; you can't rule any of those out.