I have a new iPad with the Safari browser. Safari will not run Flash Player or download the Flash Player app. Is there a solution or do I have to load a different browser?

Apple doesn't include Adobe Flash Player in the in-built Application "Safari".

You can download a 3rd Party Application like Puffin Web Browser.

Adobe does not and never has produce Flash for iOS and has now discontinued

Flash for ALL Mobile devices

Flash has not now nor ever will be on any ios devices.

There are third party browsers that redirect web sites to a server, convert the flash content and send it to your device.

They don't work very well if at all for every site.

Search the app store.

Skyfire and Puffin are alt. browsers

5 Flash Player Alternatives

http://www.techshout.com/features/2011/01/flash-player-for-ipad-apps/

Top 4 browsers supports flash player on iPad and iPhone

http://mashtips.com/flash-player-ios/