The problem is that Period is just a value - 156, it is not a delay. When you import Period from the Clock_pkgm you are just importing the definition of its value.
The only places time-unit/precision scales a values is in a delay expression #(expr), or time literal.
You should define your period as
parameter real Period = 1.56ns/1ps; // value will be in ps 1560
And use the period as
#(Period *1ps)/2 clk = !clk;