Old monitor new graphics card

Solution
That's the right kind, with an HDMI jack to plug into your card, and a port to plug your VGA cable into.

These active adapters have electronics inside to convert the signal though, and I can't say for absolute certain that you won't encounter any compatibility issue with any particular model. It may work fine, though there are some other models on Amazon that have a higher percentage of positive reviews along more reviews in general that might potentially be a safer bet, such as either of these...

https://www.amazon.co.uk/Rankie-HDMI-Adapter-3-5mm-Audio-Black/dp/B00ZMV7RL2

https://www.amazon.co.uk/Adapter-VicTsing-Converter-Desktop-Streaming-Black/dp/B016I341IY
No, that's a passive adapter for refitting an analog VGA plug to a analog DVI-I one, which use the same signal (it also appears to have the plugs going in the wrong direction). These current cards only have ports that output digital signals and don't include the hardware to convert a digital signal to analog, so you need an active adapter that can do that. It needs to convert from either DVI-D, HDMI or DisplayPort to VGA. For a DVI adapter, you need to specifically look for ones that mentions the words "active" and "DVI-D". Here are a few examples of adapters that would probably work that I quickly looked up...

DisplayPort to VGA:
https://www.amazon.com/Rankie-DisplayPort-Adapter-Plated-Converter/dp/B00Z08TZNU

HDMI to VGA:
https://www.amazon.com/VicTsing-Gold-Plated-Converter-Adapter-Desktop/dp/B016HL4CAY

DVI-D to VGA:
https://www.amazon.com/Adapter-GANA-Converter-Supporting-displays/dp/B06XFR74K2
 
That's the right kind, with an HDMI jack to plug into your card, and a port to plug your VGA cable into.

These active adapters have electronics inside to convert the signal though, and I can't say for absolute certain that you won't encounter any compatibility issue with any particular model. It may work fine, though there are some other models on Amazon that have a higher percentage of positive reviews along more reviews in general that might potentially be a safer bet, such as either of these...

https://www.amazon.co.uk/Rankie-HDMI-Adapter-3-5mm-Audio-Black/dp/B00ZMV7RL2

https://www.amazon.co.uk/Adapter-VicTsing-Converter-Desktop-Streaming-Black/dp/B016I341IY
 
Solution