That appears to be a Morse Taper Weldon style endmill holder.
The 'Weldon' part refers to the method of retaining the cutter in a precision bore with a set screw. It works fine but not all end mills have flats for the set screw(s) and this can be a problem if you plan to use solid carbide cutters unless you have a way to put a small flat on the shank of the tool.
The 'Morse Taper' part refers to the end that fits into the spindle of the machine.
You need a way to hold the cutters - yes. If you have a morse taper (MT2, MT1, etc) in your spindle, then this is one way to go. Hopefully, you don't have a morse taper in your spindle - they hold, but not that well and are a bad choice for milling in my opinion.
Do you know what taper the inside of your spindle is?
Personally, I would look into using collets if you can.