If $f(x) = x^2 - 1$ and $g(x) = x + 7,$ evaluate $f(g(7)) + g(f(3)).$
We just plug into our function definitions given in the problem:

\begin{align*}
f(g(7)) + g(f(3)) &= f(7 + 7) + g(3^2 - 1) \\
&= f(14) + g(8) = (14^2 - 1) + (8 + 7) \\
&= 195 + 15 = \boxed{210}
\end{align*}