Won a 7MM at a rmef dinner. Remington 700 SPS camo. Getting older and 3X9 scope doesn't seem to cut it anymore.
I'm thinking of a 4X16 (?) or at least something with a larger than  a 3X9 in case I'm the one drawn for an elk trip which is the other part of the ticket.
Budget can be 1500. Haven't shot the Remington yet, taking care of some old age health related issues.

I was going to suggest VX3 3.5-10X but if that isn't enough glass it makes me wonder what's going on with you eyes? An elk is not a small animal and 10X at 400yds. ought to give you a pretty usable sight picture; I guess the VX3 4.5-14X would be my suggestion then. The VX3's aren't S&B's but for hunting glass I feel they are quite adequate.

Lots of 3x12 scopes out there.  They give you the low range and a bit more magnification for the long shots.  I have a nikon monarch 3x12.  Pretty nice scope and in the 350 range so way below your budget.

The three rifles I cycle through for elk have a 2-7, a 3-9 and a 3-12. I have never needed more. My farthest shot on an elk is 250 yards. Elk present a big target. I hunt mostly in the trees where you may only be able to see 100 yards and field of view is important  so my scopes are usually set on 3 or 4 power. If you want more than a 3-9 I really like my 3-12 it has a little more on the top end but doesn't give up the bottom end. What ever you decide,look through a bunch of scopes as eye relief and field of view can vary drastically between brands.

ETA. Post 25-06

It really depends on where you plan to hunt. I normally run a 3-12 and find I don't use the 12x that much. With that said, last years hunt was in wide open areas and a 4-16 would have worked. What you need to consider is if the weight penalty, if there is one, is worth it. I have a 3-12 Burris, a 3-12 Zeiss and a 4-14 Redfield on my elk guns. They are all gtg.

Vortex Razor LH 3-15x42. Plus you'll have some $$ left over for ammo/ancillary gear.

I used a Bushnell Scopechief VI 3x9 for many years.  I used it to shoot my last elk at about 325 yds.  I find right about 5x to 5.5x setting to be ideal as l for me and thats pretty much where the scope lives.

The same will be true for the Vortex that replaced it.

I think going up in quality of glass will get you further than just upping the power of the scope.

I recently bought a vortex viper pst 4-16x50 ffp moa for my 6.5 creedmoor. It's going to be my all around hunting rifle. Got it for 650 shipped from euro optics. 

Burris eliminator III

YouTube them they kick ass

Leupold 4.5 to 14 x 50mm with reticle of your choice. Lifetime warranty and great in low light situations.

This!  
3-9x means nothing if it's not good glass or not focused correctly.  So to the op,  what scope do you have now?  Leupold 3.5-10x is all you need for elk unless you're going for 1000yds

NF 2.5-10x24

Right now I have a Cabela's Outfitter 3 X 9 on my Savage 7MM, not sure who they contracted with at that time for their scopes. Bought it around 2000 as I recall.
Don't really think it's my eyes, although I will turn 66 this year. It may have more to do with shooting the targets on the clubs 200 yard range. The bulleyes seem really small and hard to pick out. Also at 66 and needing a new scope money is less of a consideration than when I was younger and had more bills and other pressing matters. Or I could just sell the gun as a second 7MM really isn't necessary. But I hate to sell my guns.

With the win of the Remington I also am going to be one of 18 people to have a chance to win an elk hunt in Colorado. Not sure if that's just Michigan or some of the other RMEF chapters that joined in. A couple buddies have been going to the ranch that's donated the prize and they said their shots are mostly 250 to 350 yards. Humorously they finally talked me into going with them in 2018 to the ranch for an elk hunt. Never been so lucky in my life.

Some good suggestions from everyone. I'm kind of leaning towards Vortex Viper 4 X 16 X 50 as suggested by the hunter89 as I have had good customer relations with Vortex. I also am intrigued with the Bushnell Eliminator. One of the really interesting scopes with the built in range finder. Weight may play a factor. Another factor is how much longer I'm going to shoot a 7 MM. Not as gung ho to go elk hunting in the mountains as when I was younger. Those mountains don't get less steep as one gets older and the last couple years mule deer at somewhat lower elevations have been fun to hunt.

Thanks to all for the great suggestions.

this

I'm currently getting the parts together for a light-ish (finished weight of ~7.5 pounds with the optic) .300 WM build, and am probably going with the NF 2.5-10x42.  Only 19 ounces for the non-illuminated and the ability to repeatedly dial for elevation is a huge plus.

I like something in the 4-14 range.

i have been liking my SWFA ss 3-15x scope. i would recommend these to anyone. really good stuff.

SFP - $500
FFP - $700

My poor person .300WM is a Savage 111 with a Leupold 3.5-10X40. 7 pounds 15 ounces. Dang accurate for what it is.

We have found that a rolled up pair of heavy socks really tones down the recoil.

My favorite elk rifle is a featherweight Model 70 in 270 Win with a 2-7 Leupold on it, I've killed almost 50 elk with it. I have a featherweight Model 70 in 7mm Mauser with a 2-7 Leupold on it and last I have a Model 70 in 375 H&H with a 1.5-5 Leupold on it.

For about 25 years I used a 4 power Weaver on a Remington 760 in 270 Win.

I've killed a lot of elk using those low power scopes through out my life.

I guess it boils down to whatever scope lets you see what you're aiming at, is sharp and clear is the one for you.

Just about what I went with on my 300 RUM, have the NF NXS 2.5-10x32 on it. Great little glass.