The correct answer is $\boxed{s + 3}$.
A causal system is a system that responds to an input only after the input has been applied. In other words, the output of a causal system cannot precede the input.
The transfer function of a causal system must have no poles in the right half-plane. The transfer function of the given system, $H(s) = \frac{1}{s^2 + s – 6}$, has a pole at $s = -3$. Therefore, the given system is not causal.
To make the given system causal, we need to cascade it with another LTI system having a transfer function $H_1(s)$ such that the overall transfer function has no poles in the right half-plane.
The transfer function $H_1(s) = s + 3$ has no poles in the right half-plane. Therefore, if we cascade the given system with a system having a transfer function of $s + 3$, the overall system will be causal.
The other options, $s – 2$, $s – 6$, and $s + 1$, all have poles in the right half-plane. Therefore, if we cascade the given system with a system having any of these transfer functions, the overall system will not be causal.