Discord could be considered a trusted application dependant on its purpose.
One major concern I would say Discord opens up is the ability to carry out file transfer which may introduce malicious data into a network, however this risk may be no different from allowing general internet access over HTTP/HTTPS.
If Discord uses Port 443 for its text, data and voice then its no less secure than general web browsers. However it may invite a potential attack vector to be exploited.
If Discord provides some kind of centralised user management where users are created by an administrator and can be restricted to not join non-authorised Discord channels then I would not consider it any less-secure than web browsing.
The Discord desktop application may open up other vulnerabilities in the application code but this again is the same as any other 3rd party application.
In this case, it is up to your risk appetite to decide.