There are so many different codecs for phone calls and many of them have very high license fees, meaning it will take a lot of time before everyone can use normal telephony with wide band audio.
Is Opus supported for VoLTE?
The usual codecs for VoLTE are AMR, AMR-WB and EVS (see links below for more info - thanks, @Mikael Dúi Bolinder).
As with most mainstream voice (and video codecs) there is IPR and licensing associate with these. However, for end users the network providers and device manufacturers have included the licensing and the codecs in their rollouts so a typical operator service will use these.
I'm not aware of any restrictions from 3GPP on using other codecs if the devices and the network support them, but the above are definitely the default and the most widely used.
If you want to create your own voice service, e.g a VoIP service running over the data connection to the phone, then in theory you can use whatever codec you want. It's worth being aware that for software based codecs, which they will be unless they are tightly integrated in the device's hardware, the efficiency is important as an inefficient implementation may impact performance, battery life etc.
For Opus in particular there are several open source projects which provide Android libraries for this, for example. Opus is also supposed to be supported on devices from Android 5+ (https://developer.android.com/guide/topics/media/media-formats).
amr-licensing-wikipedia: https://en.wikipedia.org/wiki/Adaptive_Multi-Rate_audio_codec#Licensing_and_patent_issues "AMR licensing (and issues) on Wikipedia"
amr-wb-licensing-wikipedia: https://en.wikipedia.org/wiki/Adaptive_Multi-Rate_Wideband#Licensing "AMR-WB licensing on Wikipedia"
evs-news-patent-pool: http://www.mpegla.com/Lists/MPEG%20LA%20News%20List/Attachments/97/n-16-01-20.pdf "MPEG developing a patent pool for EVS"