In SharePoint Online, part of Office 365 offering, the way you import web parts is done differently than the traditional methods with on-premise SharePoint installations.
The way SharePoint web parts are imported with on-premise versions is you simply navigate to the web page and in edit mode, click Insert Web Part and you get presented with nice layout of web part options together with Upload a Web Part link – quick and easy.
However, in SharePoint Online environment, when you click Insert Web Part you get the following options with Silverlight control. Unfortunately, there is NO upload a web part link to be found 
.
So the way you get around this is to navigate to Site Collection Settings (or ask your Site Collection Administrator) and Web Part Galleries area.
Upload your web part file and assign the best possible group including a custom group if you wish. Once uploaded, then it becomes available to add your web part in your web page.
Hope this post saves you time if you’re faced with this situation!
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Published by Chirag Patel @techChirag
Chirag is an independent Microsoft 365 consultant at Patel Consulting, and Microsoft MVP (Office & Apps Services), based in UK with more than 20 years of industry experience. He is also a BCS (British Computer Society) Member & Chartered IT Professional, Microsoft 365 Certified Enterprise Administrator Expert, MCT (Microsoft Certified Trainer) and TOGAF9 Certified Architect.
He works with a wide variety of clients in many sectors, designing and implementing business collaboration, data and information management solutions and services based on Microsoft Teams, SharePoint and Microsoft 365 technologies, Power Platform to create business value for both themselves and their customers, including UK Microsoft Gold Partners with deployment, upgrade and migration services delivery.
Chirag is an active Microsoft 365 community participant, frequent speaker at local and international events including Microsoft 365 Saturdays, Power Saturdays, SharePoint Saturdays, Collab365, TeamsFest, Modern Workplace Summit and Scottish Summit. You can follow Chirag on twitter at @techChirag.
View all posts by Chirag Patel @techChirag
Chirag Patel MVP MCT 
THANK YOU. Saved my life 🙂
Hi, I ran into the same issue, just found an easier solution:
Temporary disable the Silverlight add-on in your browser.
Internet options – programs – manage add-ons
You will then get the “old” method to add web parts, which allows you to upload