The phrase "to request an application" means asking for a form or document that you need to fill out in order to apply for something, like a job or a program. Full definition
Once you choose a plan that meets your needs and fits your budget, you can request an application for life insurance coverage. (term-life-online.com)
By requesting the application online, you'll receive the information faster, as tenants can fill out their application anytime, anywhere from the comfort of their home. (sparkrental.mysmartmove.com)