I need iOS13.0 to work with my phone and to be download application for my phone

The following link describes how to update an iPhone:

Update your iPhone, iPad, or iPod touch - Apple Support

Given this iPhone is three or four years back (iOS 11) with no updates, and which probably means it’s also close to full, you’ll probably have to use a computer to update, which is described in the linked article.

Your update will get iOS 15.5; the current version.

This iPhone cannot run the next version of iOS, iOS 16, which is arriving later this year.

adeyemi20 wrote:

Can this current version iOS 15.5 is available to download any application

If you want to run current and maintained applications and which require current versions of iOS, then you will want to update to and will want to be running iOS 15.5. Current.

Some unmaintained apps might not or will not work on iOS 15.5. Some third-party password managers were never updated, for instance.

Any update will get you iOS 15.5. You can not update from iOS 11 to any intermediate iOS version; only to iOS 15.5.

If your data has value to you, then backups are one of the very few ways to show that:

How to back up your iPhone, iPad, and iPod touch - Apple Support

Data with no backups is one loss, one theft, one fire, one dunk, or one drop away from complete loss.

Settings > General > Software update

The current version is iOS 15.5 which is available to download.