You cannot introduce new values and functions to a module’s namespace externally without an @eval solution like @GunnarFarneback proposed, which sidesteps the issue because it evaluates the code within the module Test.
There is a standard way to extend a module in a somewhat restricted way: add methods to an existing function (what @gdalle mentioned).
julia> module A
greeting() = "hello"
end
Main.A
julia> A.greeting()
"hello"
julia> A.greeting(name) = "hello $name"
julia> A.greeting("Sergey")
"hello Sergey"