The Photos.app is a part of the system and updated by updating to a newer system version.
Or are you asking about updating your Photos Library with iCloud Photos? If you are syncing your photos with iCloud Photos, the photos will be updated, whenever your iPhone is turned on, connected to Wi-fi, and connected to a power source.
For the update to happen, you have to have sufficient free storage on your iPhone to download the new photos, you must not be running out of iCloud Storage, there must not be any problems with your iCloud AppleID. If you are getting a warning about running out of Cloud Storage, you have to fix this, before trying to sync your devices with iCloud.