I have a Mac Pro tower 2009-2012 Running Snow Lepoard I need a connector DVI to HDMI

If you can identify which Mac Pro you do have that would be handy. Go to About This Mac to get the model and year.

If it is a MacPro 4.1 2009 it can only be upgraded to El Capitan, if it is a Mac Pro 5.1 20110-2012 model it can be upgraded to High Sierra and if it has a suitable 'Metal' capable graphics card then you can upgrade it to Mojave. If it is a MP 5.1 it would need to be upgraded to El Capitan first and then to High Sierra or Mojave. Read these guides.

How to upgrade to OS X El Capitan - Apple Support

How to upgrade to macOS High Sierra - Apple Support

How to upgrade to macOS Mojave - Apple Support

There are plenty of DVI to HDMI cables out there but I don't think they carry an audio signal (DVI doesn't carry audio), so you would need to connect another cable from the Macs audio output to an audio input on the TV.

You could buy a new graphics card for your Mac which has HDMI output, you would need to make sure it is a Mac edition card or 'flashed for Mac and compatible for all the OS's mentioned above, and also Snow Leopard. This could get expensive, so decide what you want to do with your Mac. Let us know so we can advise more.

HDMI

There's a lot fo overthinking in this entire discussion:

What's true is:

You have a computer with a DVI output. DVI can be converted to HDMI without any specialized hardware as the bitstreams are the same, but there's some minor asterisks to be aware. The only assumption I'm going to make is you have a TV that is 720p or 1080p or 4k.

Find DVI -> HDMI cable, these can be had for as little as $8 and plug in. You will be able to use your computer on your TV.

Now for the asterisks. DVI does not carry 4k and when converted to HDMI is limited 1080p as Dual Link DVI (used for 1440p) requires a specialized hardware to convert to HDMI as Dual Link DVI is dual-data streams. Fortunately, this is a TV and while a few 4k TVs do support 1440p, all 4k TVs support 1080p. You're better off investing in a new GPU if you'd like higher than 1080p. You may have to configure overscan corrections if elements on your TV appear off screen. Also as mentioned, DVI will not carry audio. Even that gets a special asterisk as on Windows with the modern GPUs, DVI does (if you doubt me, you can google it. I encourage it) can output audio when using DVI -> HDMI.

Lastly, there's no GPU that I'm aware of that shipped for any Mac Pro that doesn't support 1080p, so you're in the clear there.

OS Upgrades:

As mentioned the Mac Pro 5,1 can run 10.14 Mojave but requires a GPU that supports metal. You can use PC GPUs these days in a Mac Pro like the ever popular RX580 but it will not support the pre-boot EFI screen (the screen that appears when you first turn on the computer or hold down option keys). I'd recommend going up to 10.13 at the very least. There's entire guides on Mojave and Mac Pro 5,1s. It boils down to just having a supported GPU. Upgrading to 10.13 will not require any hardware purchases.

Summary

Buy DVI -> HDMI cable. Plug into TV. Configure overscan. Also, update your OS to 10.13 at the very least so you can run modern web browsers for security and support the streaming services for your TV. Win at life.

If your Mac Pro has a video card with a standard DVI connector - which many of that time period did then a standard DVI to HDMI cable or adapter would work. See the following as possible examples.

Adapter - https://www.amazon.com/Benfei-Bidirectional-Female-Adapter-Gold-Plated/dp/B07CXY79KR/

Cable - https://www.amazon.com/Directional-Adapter-Compatible-Raspberry-Graphics/dp/B07D6RL3VN/

Being that your Mac Pro uses a PCIe video card it is possible to swap it for a newer card. However newer is going to be a relative term. The last year Apple sold a Mac which supported a PCIe video card was in 2012. Due to this being so long ago both AMD and Nvidia long ago stopped making PCIe video card which have Mac firmware support.

This lack of Mac firmware support does not make it totally impossible to fit a newer card but makes life harder and definitely means some functions are impossible to access. For example you cannot use FileVault2 encryption unless the card has Mac firmware.

The last cards that did officially have Mac firmware available were the following -

Nvidia - GTX-680 Mac Edition

AMD - EVGA Radeon HD 7950 Mac Edition

You might still be able to find one on eBay which is where I got my HD 7950 Mac Edition.

It is possible to 'flash' some newer AMD cards to have Mac firmware e.g. an AMD RX 280x. It is also possible to buy some cards flashed with Mac firmware by a specialist reseller called MacVidCards.com

Note: Apple do not support Nvidia cards in Mojave but they can be used in High Sierra.

Note: If you get a card that is too new then Snow Leopard will not support it meaning you might have to first upgrade the Mac operating system to Mavericks, Yosemite, Sierra or High Sierra as required.

Many of the cards for the Mac Pro also have a Mini DisplayPort jack.

What graphic card do you have?