You cannot buy or download new DLC on PS3. The PlayStation Store on PS3 (and PSP, Vita web store) was permanently closed July 2, 2021.
What Still Works
Previously purchased DLC: Still downloadable from Library → Purchased on the PS3 (if you owned it before closure).
Disc-based games with DLC on disc:Game of the Year editions (e.g., Fallout 3 GOTY, Borderlands GOTY, Uncharted 3 GOTY) include all DLC on the disc — no download needed.
Game updates (patches): Still downloadable (separate from Store).
What's Gone
Buying new DLC, games, themes, avatars.
Redeeming DLC codes (most expired; some may still work via web store → account → redeem codes).
In-game store links (error NP-8021-6).
Workarounds
Web Store (PC/Phone):store.playstation.com → Login → Library → Purchased → "Download to PS3" (if listed). Hit or miss.
PS4/PS5 Backward Compatibility: Many PS3 games with DLC are on PlayStation Now (cloud streaming) via Premium tier — includes all DLC. Or remasters (God of War Saga, Uncharted Collection, Bioshock Collection).
Physical GOTY Editions: Hunt eBay / local stores for "Complete / GOTY / Ultimate / Legendary" editions.
Custom Firmware (HEN / CFW): On hackable PS3 (3.55 OFW or lower, or HAN on 4.82+), you can install .pkg DLC files from community archives (e.g., PS3Xploit, Brewology). Legal gray area; ban risk if online.
For 99% of users: Buy the GOTY disc or stream via PS Plus Premium. The native store is dead.