Mixing Ca(OH)2 with Ca(NO3)2
Not much is going to happen. Due to low solubility of $\ce{Ca(OH)2}$, further suppressed by the presence of calcium cations from the dissolved $\ce{Ca(NO3)2}$, you get a suspension of calcium hydroxide, which unfiltered looks like white cloudy liquid and is also known as milk of lime.



Regarding the $\mathrm{pH}$ if the solution, $\ce{Ca(NO3)2}$ is prone to hydrolysis and alone would create slightly acidic medium:

Step 1:

$$
\begin{align}
\ce{Ca(NO3)2 + H2O &amp;&lt;=&gt; CaOHNO3 + HNO3} \tag{R1.1}\\
\ce{Ca^2+ + 2 NO3- + H2O &amp;&lt;=&gt; CaOH+ + 2 NO3- + \color{red}{H+}}\tag{R1.2}\\
\ce{Ca^2+ + H2O &amp;&lt;=&gt; CaOH+ + \color{red}{H+}}\tag{R1.3}
\end{align}
$$

Step 2:

$$
\begin{align}
\ce{CaOHNO3 + H2O &amp;&lt;=&gt; Ca(OH)2 + HNO3}\tag{R2.1}\\
\ce{CaOH+ + NO3- + H2O &amp;&lt;=&gt; Ca(OH)2 + NO3- + \color{red}{H+}}\tag{R2.2}\\
\ce{CaOH+ + H2O &amp;&lt;=&gt; Ca(OH)2 + \color{red}{H+}}\tag{R2.3}
\end{align}
$$

(Here .1, .2, .3 stand for molecular, complete ionic, and net ionic equation, correspondingly.)

But, when you add enough $\ce{Ca(OH)2}$ (saturated solution), which is a strong base:

$$\ce{Ca(OH)2 &lt;=&gt; Ca^2+ + 2 \color{blue}{OH-}}\, ,$$

I'd expect the resulting solution to be basic.