Was this ship the one used to film the Hornblower series a few years ago?
No, this is a new ship. The Hornblower series used the Grand Turk, a Turkish built replica of a 1741 vintage Royal Navy 6th rate frigate. While the ship has a good appearance, the construction methods are largely modern. The Hermoine is built as closer to original as is possible with currently maritime regulations. The Grand Turk has been renamed and is in France.
The ship used in Master and Commander is a replica of of a Royal Navy Revolutionary era 6th Rate 24 gun frigate, HMS Rose. That ship is moored in San Diego.