In an operator sharing environment how new operator will get the IMSI and other Identity from other network HSS?

Question

Because your identity will be registered in Home HSS and while roaming how other operator will get these information

Answer 1

If an operator has roaming agreement with another operator then users of first operator can gets services through second network operators. In case of LTE network, when different PLMN users try to get LTE services through another operator network, they can get LTE services if both the operator has roaming agreement in place.
In this case, when UE sends attach request to MME of the visited network, it contacts to HSS of other network based on the information it receives from UE. Visited network MME and Home network HSS would exchange the details using Diameter based S6a interface.
Fetching the details such as Authentication Vector, Security Keys parameter would be as same as it happens in home network case where MME and HSS both resides in home network.