Hook: Wall Medium (Blue Square)The Battle-Worn Republic Placard decoration fits into a blue medium square wall hook.
Hook: Wall Large (Purple Rectangle)The Battle-Worn Republic Placard decoration fits into a large purple rectangle wall hook.
How to Get a Battle-Worn Republic Placard Decoration
Cartel Pack Decorations
The Battle-Worn Republic Placard decoration can be dropped from Seneschal's Stronghold Packs, which were released on the Cartel Market and bought with Cartel Coins. Cartel Packs, including the Seneschal's Stronghold Pack, include a random selection of items from the Seneschal's Stronghold collection of items. You aren't guaranteed to get a Battle-Worn Republic Placard decoration from a Seneschal's Stronghold Pack, but it is one of the few ways to get a Battle-Worn Republic Placard deco apart from buying it on the GTN from another player.
If you're looking to get a Battle-Worn Republic Placard, the easiest way to get it is to head to the Galactic Trade Network (GTN) in SWTOR and buy it with credits from another player. If it's very rare and not available on the Cartel Market, you could try buying from the GTN and hope you get it.