Hook: Ship Hook (Giant Purple Square)The Damaged Republic ATV decoration fits into a ship hook (Nar Shaddaa, Tatooine and Yavin 4 only).
How to Get a Damaged Republic ATV Decoration
Cartel Pack Decorations
The Damaged Republic ATV decoration can be dropped from Underworld Alliance Packs, which were released on the Cartel Market and bought with Cartel Coins. Cartel Packs, including the Underworld Alliance Pack, include a random selection of items from the Underworld Alliance collection of items. You aren't guaranteed to get a Damaged Republic ATV decoration from a Underworld Alliance Pack, but it is one of the few ways to get a Damaged Republic ATV deco apart from buying it on the GTN from another player.
If you're looking to get a Damaged Republic ATV, 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.