On Peace
Triple Kingdom
England, Scotland, and Ireland—the United Kingdom after the 1801 Act of Union. Keats is writing in the immediate aftermath of political consolidation.
Mountain nymph
Liberty personified. The phrase echoes Milton's "L'Allegro" where the mountain nymph is Liberty herself—Keats wants Peace and Liberty together.
Sceptred Tyrants
Napoleon was defeated in 1814, but the Congress of Vienna was restoring absolute monarchs across Europe. Keats fears Europe will return to pre-revolutionary tyranny.
Give thy Kings law
Constitutional monarchy—make kings subject to law, not above it. This is radical politics in 1814 when monarchs were being restored with full power.