looks like bad architecture all the way. also you have not specified the type of app you need to notify to (web app / console app / winforms / service etc etc)
nevertheless, to answer your question, there are multiple ways of solving this. you could use:
1) timestamps if you were just interested in ensuring the next set of updates from the second app dont conflict with the updates from the first app
2) sql dependency object - see http://msdn.microsoft.com/en-us/library/system.data.sqlclient.sqldependency.aspx for more info
3) a custom push notification service which multiple clients (web / winform / service) can subscribe to and get notified on changes
in short, you need to use the simplest and easiest and cheapest (in terms of efforts) solution based on how complex your notification requirements are and for what purpose you need to use them. dont try to build an overly complex notification system if a simple data concurrency is your only requirement (in that case go for a simple timestamp based solution)