Can I add a new album to my iCloud?

Create album from iPhone it will reflect in iCloud Use albums in Photos on iPhone - Apple Support

Read Organize and find your photos on your iPhone, iPad, or iPod touch - Apple Support

Using a Mac you can create an album from photo application , it will automatically sync in www.icloud.com

See the articles Create and work with albums in Photos on Mac - Apple Support

Organise photos and videos in albums on iCloud.com - Apple Support

Create an album

1. In Photos on iCloud.com, hold the pointer over My Albums in the sidebar, then click .
2. Choose New Album, enter a name for the new album, then click Save.

To view the album, click My Albums in the sidebar, then click the album name.

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"Can I add a new album to my iCloud?"

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Use iCloud Sharing:

If you want to create a collaborative photo and video album, use an iCloud Shared Album. This is to share it among two or more devices.