There are University provided services which allow sharing of files with local and external users (DataSync, OneDrive, Globus and SharePoint). These should be used in preference to sharing files by email as who has access can be checked, removed and changed as required. Once data is sent as an attachment you no longer have any control over access.
If third-party sharing services are the only option due to collaboration requirements then encryption must be used and a risk assessment should be performed and accepted by the School/Unit. The data should be deleted from the sharing service once accessed to reduce the window of opportunity. Arrangements should be made with the recipient of the data to ensure that this window is as small as possible.
If the only option is to use email then the data should be sent as an encrypted file or in an encrypted container. The password for this file/container should be provided by a different mechanism to the file - if the file has been emailed then the password should be passed by phone, for example.
When encryption is used an appropriate mechanism usable for both parties should be agreed in advance.
For all sharing mechanisms, whether cloud or email, it should be ensured that the data is only shared with those who need the data. It should be confirmed that the users being given access are the correct users and not anyone with a similar name or role. Sharing with groups, mailing lists or any mechanism where it may not be clear specifically who will receive and have access to the data should be avoided.
The responsibilities of the recipients of the data should be made clear in any agreement to share data.
Remember that if someone can view data then they can take a copy of that data. There is no technological way to prevent this, even if a product or service claims that is the case. At minimum a screenshot or photograph with another device will always be possible, so even if access is revoked at a later date the data may still be held by the recipient.