Iphotos

Can we assume you have iCloud Photos enabled and that you have not reached the limit of your iCloud storage? Check to make sure both of these are in place first.

Next, you'll want to make sure that the photo library you're using in Photos for Mac is set as your system photo library. Check this in the Photos preferences on the General tab. If the button to set it as your system library looks like it can be pressed, then it isn't already and a different library is. You might want to resolve that discrepancy before clicking the button otherwise you could end up with duplicates.

Lastly, iCloud Photo syncing isn't lightning fast. I don't know how much you've done, but if you've brought in a bunch of imported photos, it could take a while to sync and it would be largely dependent on your internet upload and download speeds.

But if it still isn't syncing or is going very slowly, I guess I'd check to make sure your iPhone's iCloud Photo settings are set to Optimize Storage so that it isn't downloading full copies of all of your photos which takes longer and could fill up your iPhone's storage.

Just be mindful that if you've got photos on your iPhone that are synced with iCloud and a library on your Mac that isn't and you turn that syncing on, you could end up with duplicates. Generally, iCloud Photos tries to avoid these but it can happen. It's not like I'd have a better suggestion in such a case but I wanted to manage your expectations.