It is important that you have control over the gallery at a member group level, in order to be able to restrict how much a user do in the gallery.
In Invision Community 4, there are settings within each of your member groups for this purpose in Members>Members>Groups
From here you will see that you can add or remove limitations from member groups for things such as the ability to create albums or upload movies, in addition to restricting the amount they can upload.
When switching on some of these settings, you will have other options that will appear, giving you yet more control over what your members can and cannot do within your gallery. In the example below I have checked the "Can create albums?" option which has now given me more granular settings in this area.
When gallery is installed, when editing a member in the admin CP, you will also be able to see statistics related to what that user has contributed to the gallery.