You have two options:

1) Run PostgreSQL inside your Codespace (recommended to start)

• Add a devcontainer feature for Postgres and forward port 5432. This gives you localhost access from apps and psql inside the codespace.
• Example devcontainer setup:

{
  "name": "Codespace + PostgreSQL",
  "features": {
    "ghcr.io/devcontainers/features/postgres:1": {
      "version": "16",
      "password": "postgres",
      "database": "appdb"
    }
  },
  "forwardPorts": [5432],
  "remoteEnv": {
    "DATABASE_URL": "postgresql://postgres:postgres@localhost:5432/appdb"
  },
  "portsAttributes": {
    "5432": { "label": "PostgreSQL", "onAutoForward": "silent", "requireLocalPort": true }
  }
}

• After the codespace rebuilds, connect with:
  • Inside the codespace: psql "$DATABASE_URL"
  • From your app: DATABASE_URL=postgresql://postgres:postgres@localhost:5432/appdb
• Tip: In VS Code, forward port 5432 to use local tools (TablePlus, psql) against the DB running in the codespace.

2) Connect to an external PostgreSQL server

• Make sure your DB allows connections from the internet (or via a bastion/SSH tunnel you control).
• Store secrets safely (Codespaces secrets or environment variables), then connect with a standard connection string:
  • psql "postgresql://USER:PASSWORD@HOST:PORT/DBNAME?sslmode=require"
  • Or set DATABASE_URL and have your app read it.
• If your DB is firewall-restricted to specific IPs, note that Codespaces don’t have a fixed outbound IP; use a proxy/SSH tunnel or host Postgres inside the codespace instead.

Common pitfalls

• Use localhost when the DB runs in the same codespace.
• Forward port 5432 in the devcontainer to make it accessible to your local tools via VS Code port forwarding.
• Keep credentials out of source control; use Codespaces/Repo secrets or environment variables.

if it's local development, running PostgreSQL inside the Codespace itself is usually enough, no need to connect to an external or separate PostgreSQL server,

so unless you have a very specific reason to still connect to your own PostgreSQL,

PostgreSQL can be installed and configured directly inside the GitHub Codespace since Codespaces are basically full-featured cloud dev environments running on Linux containers, I even have my Public Templates for anyone to use, and you can have your own too,

https://github.com/jfullstackdev/codespaces-template-laravel

https://github.com/jfullstackdev/codespaces-template-mern

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