an age-old royal challenge
a very old problem or puzzle for people in the royal family
to fulfil your destiny
to do what you were born or
destined3 to do (for example Prince William was born to be King)
pursuing
trying to do or achieve something, usually over a long period of time
he's patron of
he's a very important supporter of
to improve their self-confidence
to make them feel more confident about their own abilities and themselves, to give them a more positive attitude about what they can do and achieve
to make a difference
to make things better, to improve them
there's a time and a place for being an ornament
while it's appropriate at certain times to be someone that people want to look at, to be on display, at other times, it isn't. (An ornament is an object that is nice to look at but not very useful)
being at an engagement
attending a public function
actually doing stuff
being
actively4 involved, participating (rather than just being an observer)
doing a slightly different angle
thinking about things in a different or unconventional way (note: the usual expression is 'coming at it from a different angle')