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Choice D is correct. To express $n$ in terms of $p$, the given equation must be solved for $n$. Subtracting $9$ from both sides of the given equation yields $p-9=\frac{14}{n}$. Since $n$ is not equal to $0$, multiplying both sides of this equation by $n$ yields $\left(p-9\right)\left(n\right)=14$. It's given that $p>9$, which means $p-9$ is not equal to $0$. Therefore, dividing both sides of $\left(p-9\right)\left(n\right)=14$ by $\left(p-9\right)$ yields $\frac{\left(p-9\right)\left(n\right)}{p-9}=\frac{14}{p-9}$, or $n=\frac{14}{p-9}$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.