It's not an application process as such.
If EE decides to improve coverage in a given area, they will search for potential locations - ones that satisfy coverage & other technical requirements, where various legal & access agreements are likely to be achieved, and where local authority planning consent is not likely to be hindered. An interested landlord is part of this process.
Once an approved site design is established, local authority planning consent & legal agreements have to be secured before a site can be progressed to build.
Depending where you are in the UK, you may want to read about the Shared Rural Network & Scottish 4G Infill projects, in which EE are prominent.
https://srn.org.uk/ & https://www.gov.scot/publications/scottish-4g-infill-programme-progress-update/
