How does a young stick insect regrow a lost leg?

Answer: A new leg forms under its skin and appears when it molts

A new leg forms under its skin and appears when it molts ✓ — A young stick insect grows by molting, shedding its outer skeleton several times. After losing a leg, it builds a new one under the old skin, and the leg appears, often smaller at first, at the next molt; adults no longer molt, so they can't regrow legs.

The stump grows a full new leg within a few days — A lost leg doesn't regrow in days; the new one shows up only at the next molt, which can be weeks away. It may take more than one molt to reach full size.

It carries spare legs stored inside its body — Stick insects don't carry spare legs inside them. The new leg is built from the cells at the stump, then revealed when the insect sheds its skin.