See the article If your iCloud Photos aren't syncing to your device - Apple Support
If your iCloud storage is full or almost full
If you exceed your iCloud storage limit, photos and videos won't sync to iCloud and your library won’t stay up to date across your devices. To continue using iCloud Photos, you can upgrade your storage plan or reduce the amount of storage that you're using.
Note : it's not necessary the old photos months back are still on iCloud server , they were not saved as iCloud storage was short , now you decided to upgrade the iCloud storage a sufficient space must be there , you need to check the status of iCloud storage Check your iCloud storage on any device - Apple Support
once iCloud storage is sufficient , if you upload new photos / videos they will sync with other devices ( iPhone / iPad ) Access and view iCloud Photos on your iPhone, iPad, or Mac - Apple Support in which photo library is set ( turned as on ) Set up and use iCloud Photos - Apple Support