I connected bank link , but Quickbooks was able to dowwload transactions from 02.03.20 ONLy.

Welcome to the Community, @helen-nguyen. Glad to know that you're able to connect your bank with QuickBooks Online. 

Let's manually update your bank to make sure we'll get the latest available transactions by going to the Banking menu, then select your bank and click Update. 

Should you see a prompt about additional authentication, simply follow the onscreen instructions. If you see specific bank errors, you can refer to Step 3: Fix specific banking errors outlined in this help article: What to do if bank transactions won’t download or there's a bank error. 

I'd also appreciate it if you can provide the specific name of your bank so we can check our reports and updates.

Feel free to message again if you have additional concerns. We're always delighted to help.