There are numerous calibers and cartridges that will fill that bill -
7Rmag
7PRC
280 or AI
7WSM
7RUM
28 Nosler
284 Win
30-06 or AI
300WinMag
300SAUM
300PRC
300WSM
300RUM
338's
etc, etc, etc
For elk size at 1,000 and plus, I typically use the 300RUM's and 338's, but at shorter ranges, I have hunted with 25-06's, 260AI's (not legal for you), 270Win, 30-06, etc, etc and even handguns.
I've never been a fan of bureaucratic and arbitrary caliber size for hunting anything, as there are many "calibers/cartridges" that would be legal that are far less viable than many that are smaller caliber but in better cartridges and bullets. I.e. a 30-30 or 303 Savage would be legal, but the 25-06, 260, 260AI, 6.5PRC, etc would not.