What is older the Royal Navy or Royal Army?

The Royal Navy first came into operation in the early 16th century but the British (or Royal Army) was set up in 1707. So therefore the Royal Navy is the oldest. Hope this help you!

Addendum:

The UK does not have a Royal Army. The navy and the air force are Royal, but the army is just the British Army.

We do have various regiments and corps that are Royal though.