Best to keep an eye on Compatibility Lists.
Master Compatibility List: http://www.veritas.com/docs/000033647
While you are waiting, please shedule upgrade to latest 8.1.x version.
Veritas will only add support in upcoming 8.1.x version, not for 7.7.x.
Veritas has not yet announced support for Exchange 2019. I think it has schema changes that may cause problems for GRT with existing NetBackup releases. Your chances are better for database level backup and restore, but I haven't tried it. I don't have inside knowledge regarding the support plans. As personal opinion, I expect GRT support to begin with the next release, and I do not expect such GRT support to get retrofitted to 8.1.2, much less 7.7.x.
Exchange 2019 CU1 was only released last week. I don't know whether it has changes that complicate supportability of backup and restore.
As @Marianne said, watch the compatibility lists. I'll bug someone internally, but it would not be appropriate for me to pre-announce plans.
I do not see any issues with NetBackup 8.1.1 and Exchange 2019, for database backup and restore. Try it in your development environment, but don't put it into production until our QA has finished testing.
I am sure that GRT restore will not work until the next NetBackup release. It would take a large effort to backport the adaptation in our code to make it work in 8.1.x. I think GRT backup will work. You can try it in your development environment but don't depend on GRT restore until your clients are on 8.2.
I have been communicating with the development and QA team. You may have seen in the SCL that they just completed validation of the latest CU's of Exchange 2013 and 2016. That does include GRT backup and restore. I am hoping for results from them regarding Exchange 2019 database restores.
I do not have any news. My unofficial expectation is that NetBackup 8.2 will support Exchange 2019, but I haven't asked the development or QA engineers about it recently. I do not expect the code that adapts to Exchange 2019 to be backported to NetBackup 8.1.x.