Yes, if you are within an academy trust, and the other school(s) use Educake, then you can do this.
You can use template tests to have one central person create standardised tests for other teachers at your school and academy trust to assign. Here's information on how to create these:
Once the template has been created, it can be found under "Saved Template Tests" in each course on your My Educake page. Here's an example of this:
You can then change the template from being shared within your school to being shared within your academy trust.
You can do this by clicking the text under the shared column, circled below.
After clicking this, your test template will then appear to all schools who are part of your academy trust, as well as those within your school account.
If you want to find out more about how to share tests between your school locally, read the article below: