There's a Service Rifle league that shoots at the Spruce Grove Gun Club. Bear in mind that the Spruce Grove range is limited to 300 yards.
If you have a service rifle with iron sights (e.g. an AR-15 or a Lee Enfield, a Garand or a Norinco 305), the next match is April 23rd. (If you don't have anything appropriate, show up and there's always someone who will lend you a rifle to shoot the match - it's 40 rounds). Alternatively, bring your scoped rifle and shoot the match for fun. The next Service Rifle match at Spruce Grove is April 23rd (first shot at 11 am).
The next "Sharpshooter" match is on May 28th. At that match you can use any firearm with any sight (targets at 100, 200 and 300 yards).
Spruce Grove also has the Swiss Rifle club, which shoots every month, usually on a Saturday.
To get out further you'd need to go to the Genesee range, which goes out to either 700 or 800 yards (call Lock and Load if you want more details on that range).
I understand that there's also a service rifle club that shoots down around Calgary at a range that is six or seven hundred yards. Don't know anyone connected to that club though. There's probably someone on this forum who is familiar with that group.