HI, new to power apps. I'd like to link an app to our mysql database running on an AWS server. I know I can use an On premises data gateway but I don't really want to rely on a pc in the office or indeed a PC at all. Is there any way this can be hosted as a service somewhere?
No, unfortunately it's not possible to do this without an on-premise gateway.
The other option you could consider is to write your own web service that exposes the MySQL data from your AWS server. You can then connect to this web service using a custom connector from Power Apps.
If it's just read-only access that you need, you could possibly write some third-party process that synchronises your MySQL data with a data source such as SharePoint.