Add the expressions.

To add the two expressions, we will first align like terms and then combine them. Here are the two expressions:

Expression 1: \(-3k + 4k^3 - 2\)

Expression 2: \(9k^2 - 3k^3 + 4k - 3\)

Now we'll rewrite them and group the like terms:

\[
\begin{align*}
\text{Expression 1:} & \quad -3k + 4k^3 - 2 \\
\text{Expression 2:} & \quad -3k^3 + 9k^2 + 4k - 3
\end{align*}
\]

Now, we'll combine them:

\[
\begin{align*}
(4k^3 - 3k^3) & + (9k^2) + (-3k + 4k) + (-2 - 3) \\
= (4 - 3)k^3 & + 9k^2 + (4 - 3)k + (-2 - 3) \\
= 1k^3 & + 9k^2 + 1k - 5
\end{align*}
\]

Finally, we can write it in standard form:

\[
k^3 + 9k^2 + k - 5
\]

So the sum of the expressions is:

\[
\boxed{k^3 + 9k^2 + k - 5}
\]