The best way to share video content to other college users (staff and students) is to uploaded it to the Stream service - https://web.microsoftstream.com/
All staff and students have access to this service both on and off campus but no one outside of the college can access any content uploaded within our tenancy
https://docs.microsoft.com/en-us/stream/portal-upload-video
If you need to restrict a video to a smaller audience (rather than the complete college - by default) this can also be done by applying permissions either using group/channels or directly on each video after you have uploaded the videos
https://docs.microsoft.com/en-us/stream/portal-permissions
Please note that like all video streaming services, uploading times can vary and take a while especially if the video files are big