Solution:

Option(D) is correct.
To Find: The value of $\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)$
Now, let $x=\frac{\pi}{3}-\sin ^{-1}\left(\frac{-1}{2}\right)$
$\begin{array}{l}
\Rightarrow x=\frac{\pi}{3}-\left(-\sin ^{-1}\left(\frac{1}{2}\right)\right)(\because \sin (-\theta)=-\sin (\theta) \\
\Rightarrow x=\frac{\pi}{3}-\left(-\frac{\pi}{6}\right)\left(\because \sin \frac{\pi}{6}=\frac{1}{2}\right) \\
\Rightarrow x=\frac{\pi}{3}+\frac{\pi}{6} \\
\Rightarrow x=\frac{3 \pi}{6}=\frac{\pi}{2}
\end{array}$