Is this dangerous???

[OakLeaf]

To say it another way: small space between the bolt holes in your handlebar clamp = normal and necessary for safety. Space between the mating surface of the clamp and the bar itself = NOT normal and not safe. They should fit seamlessly like nested spoons.

You can't see between the clamp and the bar from the angle of your picture, and you may not be able to get a good photo of that angle, but you may be able to eyeball it.

What makes ridebikeme suspicious, I think, is what you said about how your old bars were "much thinner." It's hard to tell what you mean by that. If you don't have a caliper to measure the diameter, you can do a quick-and-dirty comparison by wrapping a tape measure around the mating surface for the clamp on both bars. If they're not the same circumference, they can't use the same stem. (Don't bother measuring the bars anywhere else - often the mating surface in the center is a different diameter from the parts of the bars that your hands go on - even though I don't see any taper in your picture, best to know for sure.)

If it turns out they're not the same size, you'll probably need a caliper to find out what size you need, but if you don't have one, your LBS can measure for you.

[Seajay]

Is the gap equal at the top and the underside of the stem? If the lower gap were smaller, it would cause that slightly oversize gap at the top.
That gap looks "largish" but reasonable.... but getting it checked to be sure is good advice.
Easton Stem?

[Jordyne]

Thank you guys for the help! It seems secure but I'll ride it to the shop to check. I cannot find any size indication on the bars but the stem says 8m?

Seajay- you hattin on the Easton?!

[Seajay]

Seajay- you hattin on the Easton?!

Not at all. Just a guess at the brand of stem it was.
Sorry, I ran my comments together.