It is possible to run a v11 client against a v10 database, with some limitations.
I'm not sure I see the point though. Typically the hardest part to upgrade is the client side, e.g. due to application-compatibility issues, use of new reserved keywords in old code, dependencies on old frameworks, inability to recompile, etc. If you can upgrade the client side to 11.6.3, what would prevent you from also upgrading the database to v11? That part should be easy.