Wing Sharples and centre Trinder, both 20, were part of the England squad that reached the final of the Junior World Championships in Tokyo last June, while Burns, 19, is in line to start for England at fly-half in next month's U20s Six Nations Championship.
Today's news follows last week's announcements that senior players Nick Wood, Alasdair Strokosch and Scott Lawson have all extended their current deals with the club.
Head Coach Bryan Redpath said:
"I'm really pleased to have sorted out these contracts. It's important that as a club we develop and retain the best young talent, and all three of them have so much potential to play a big part in Gloucester's future."
"Freddie has stepped in at fly half this season and showed maturity beyond his years, Charlie can't stop scoring and Henry is a class act in the centre."
"They all have things to work on but they're all committed to improving their game and I hope they'll be a feature of Gloucester sides for many years to come."
There will, of course, be a potential opportunity to see Burns and four of his Gloucester team mates in international action at Kingsholm over the next few weeks.
Gloucester Rugby are proud to be hosting England's home games in the RBS U20s Six Nations in 2010.
England, whose squad features five players from Gloucester Rugby, will kick off the tournament at Kingsholm against Wales on the evening of Friday, 5th February (7.45pm) and then return on Friday, 26th February (7.45pm) to face Ireland.
Book your tickets by calling the ticket hotline on 0871 871 8781 option 2 or by clicking here
England RBS U20 Six Nations 2010 fixtures
February 5: England U20 v Wales U20 (Gloucester)
February 12: Italy U20 v England U20 (San Dona Di Piave)
February 26: England U20 v Ireland U20 (Gloucester)
March 12: Scotland U20 v England U20 (TBC)
March 19: France U20 v England U20 (St Nazaire)