I have a brand new Ampeg Venture 2x12 speaker cabinet for my bass guitar that hisses when the slightest bit of signal comes through.

I have my bass guitar plugged directly into a Laney Digbeth amp head, which then runs to the cab.

The hiss isn’t controlled by volume or drive whatsoever. It stays at the same frequency throughout and is only heard when I actively play my bass.

I realize that cabs usually hiss in some way no matter what, but I feel this is unusually loud. It’s annoying when I’m playing at a low volume or micing the cab.

Does anyone have any tips for me to reduce the hiss or get rid of it?

Welcome! While there are many very technically competent people that participate in the "Remote Possibilities" forum, we are mostly discussing remote recording here. Your question would probably get more responses in the "So Many Guitars, So Little Time" forum or in "GeekZone".

Speakers by themselves don't hiss. They project the hiss of your amp. Did you play the amp before with a different cabinet? Did it have a tweeter?

I’ve previously used the Laney Digbeth with an SWR Bigfoot cab and I had the same hissing issue. The SWR had a tweeter, the Ampeg does not.

Ok, thank you

You were writing
"The hiss isn’t controlled by volume or drive whatsoever. It stays at the same frequency throughout and is only heard when I actively play my bass. "

So that means, there is a hiss, when you play, but it goes away, when you don't play, while your amp is still on? Are you sure, the hiss is not coming from your bass? I know a hiss in that way from a dying battery in a bass with active electronics.
Can you use a different bass or guitar or any other instrument or playback device, that you can connect to your amp and check if the hiss is still there?

With "frequency" I guess your mean frequency band, so some kind of narrow filtered noise, but not one single frequency, that you could identify as a pitch, that you could sing or whistle?

I’m sorry, I should have been more specific on the frequency. It stays at the same pitch throughout; it’s not a band. Also, I have used my Fender Jazz bass, a passive non-battery guitar, and a Sterling Stingray, an active battery guitar (currently doesn’t have a battery in it), and the cab produced hiss, seemingly at the same pitch, with each. Let me know if you would like a video demonstration.

Sure. A demonstration can't hurt.