See details of old sessions
No, SQL Server doesn’t keep a history of session activity, imagine how fast that would grow! Your only hopes for retrieving this information from the past, as your question asks, I think, are:


That the app does something that gets logged in the default trace (and those events haven’t rolled away);
Errors that the app might have generated that clearly indicate the server it connected to ended up in the application machine’s event log; or,
Errors that the app might have generated (like deadlocks, I/O warnings, or failed logins) have been captured in the SQL Server error log or the system_health session.


Now, as mentioned in the comments, you could of course set up something to capture this activity in the future, so you don't have to sit around and wait to repeatedly hammer F5 when the app is running. You can use a variety of things, or even a combination, depending on whether you care only about connections, only about write activity, only about access to specific tables or databases, etc.:


Extended Events
logon triggers
DML triggers
SQL Server Audit
server-side trace
Wireshark
maybe even from the plan cache