The advertisement assured the public that the medicine would give back to the users, their youthful vigour and appearance.

One word substitute is Rejuvenate.

Rejuvenate: make (someone or something) look or feel better, younger, or more vital.
Restore: bring back or re-establish (a previous right, practice, or situation).
Replenish: fill (something) up again.
Render: provide or give (a service, help, etc.).