I don't see any transactions on the starling account before the 7th of May 2020, while I am doing my accounts from April 2019

We can refresh the connection to download missing transactions, hello-oktrythisn.

You can manually update your bank account to get the missing transactions. Let me show you how:

1. Log in to https://selfemployed.intuit.com/.
2. Click the Gear icon at the upper-right and click Bank accounts.
3. Toggle the account to update and click Refresh.

Then, you can go to the Transactions page and filter the list to the specific date range to find the missing transactions. If transactions aren't downloading still, you can manually add older bank transactions into QuickBooks Self-Employed. 

Keep me posted if you have other questions. You take care and have a great day!