The phrase "last application" refers to the final opportunity or use of something, especially in regards to job or admission applications. Full definition
I am able to access last application used — documents to go and opera mini but nothing more. (blog.the-ebook-reader.com)
Kennels are open daily Monday through Friday from noon to 6 pm; Saturdays 10 am to 6 pm; and Sunday 11 am to 6 pm (last application accepted 15 minutes before closing). (magic925.com)