Triggers or views on frequently updating table

If you want this query gangsta fast create an indexed view that groups on [OpenTimeUtc], [SubscriberId]. That view will serve the date filter perfectly and it will pre-calculate the distinct as well. The query will result in a plan that does an index range scan on the view. Not possible to do any better than that.

I am assuming you are trying to implement some basic replication using a trigger. As long as your process remains fairly simple, this should work OK.

However, I would advise you to read up on (i.e. google) why executing stored procedures from triggers is not a good idea, and also about SQL's built in transactional replication feature. Here is a practical guide to the 2nd topic: http://www.sql-server-performance.com/2010/transactional-replication-2008-r2/

Having said that, here is what I think should work:

USE [database_name]
IF EXISTS (SELECT 1 FROM sys.triggers WHERE name = N'trigger_name')
BEGIN
  THROW 51000, 'The trigger [trigger_name] already exists.', 1;
END
ELSE
  CREATE TRIGGER [trigger_name] ON qf.customer_working_hours
  AFTER INSERT, UPDATE, DELETE AS
  BEGIN
    SET NOCOUNT ON
    EXEC [procedure_database].qf.ServiveRefreshCustomer_WH
  END
BEGIN
END

EDIT: Updated trigger if exists check from Aaron's suggestion below.