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To make your example work, you should add [`Type=oneshot`](https://www.freedesktop.org/software/systemd/man/systemd.service.html#Type=) and [`RemainAfterExit=true`](https://www.freedesktop.org/software/systemd/man/systemd.service.html#RemainAfterExit=) to the `[Service]` section.
This way the unit won't be considered active until the curl has actually succeeded, and either won't go inactive afterwards.




However, this is somewhat unorthodox way of going about it. One would expect `website.service` to really manage the service process, and not be just a proxy for it (using curl in this case).

Instead you could just add the unit actually managing the server process as a dependency to your other units. E.g. on Ubuntu your website might be running on Apache:
```systemd
[Unit]
Description=A thing requiring the website
Requisite=apache2.service
After=apache2.service

[Service]
...
```
[Requisite](https://www.freedesktop.org/software/systemd/man/systemd.unit.html#Requisite=) makes starting the unit simply fail if Apache isn't running. It won't try to start it (as unwittingly starting web services can lead to security issues).