Sorry, I suspect not - it appears to be a VGA to RGB (Red, Green, Blue) video adapter - wrong direction and wrong video format. The Pi's yellow RCA connector outputs composite video & synch signals IIRC.
If one of your existing monitors supports DVI input then all you need is a HDMI to DVI cable or adapter - they're also "quite cheap". Otherwise it's a (oldish) TV with either Yellow (video) Red & White (audio) RCA connectors or a SCART input - see the bottom of this page (http://www.cpmspectrepi.webspace.virgin ... stKit.html
)for a picture of suitable cables - other variations are possible.
Still running Raspbian Jessie or Stretch on some older Pi's (an A, B1, 2xB2, B+, P2B, 3xP0, P0W, 2xP3A+, P3B+, P3B, B+, and a A+) but Buster on the P4B's. See: https://www.cpmspectrepi.uk/raspberry_pi/raspiidx.htm