why is it that the restoring force comes into action only after the applied external force is removed, from an elastic body?
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The restoring force of a spring is always in action. When you stretch a spring from its equilibrium point with a constant force, the spring begins to stretch. Since the restoring force is proportional to to the extension, then there will come a point where the restoring force will equal the applied force. The system is then in equilibrium If you then remove or reduce the applied force, then the spring seeks a new equilibrium position, so that the restoring force equals the new applied force (or lack of it), and so its extension reduces (or goes to zero for no applied force). In this respect, the restoring force is equal and opposite to the applied force (which creates the extension or compression), and hence why it is always in operation for any applied force, not just when the applied force is removed.