One option:
julia> module Foo
myfunc(x) = println("Foo original");
end
Main.Foo
julia> import .Foo.myfunc as foo_func
julia> foo_func(1)
Foo original
julia> myfunc(x) = println("Extended", foo_func(1))
myfunc (generic function with 1 method)
julia> myfunc(1)
Foo original
Extended