There are two basic collet closer types, those with a drawbar and those with a draw tube. The draw bar is solid and AFAIK only works with MT and R8 collets. The draw tube type may be just like the draw bar only it uses a hollow tube. Or may be more complicated and uses a lever operated assembly mounted on the left end of the headstock to pull on the draw tube to close and open the 3AT (and a lot of similar types) collets. In addition to the closer (both types), one other part called a collet closer adapter is common to all types. Externally, this has a (in your case) stub 3MT taper and a larger diameter shoulder of flange used for removing the adapter from the spindle. The ID is a close fit to the OD of whatever type collet it is made for, and should have an internal key to keep the collet from trying to spin inside the closer. This part will fit any make machine with the right spindle nose taper.
Downloads under Atlas has the parts and operating instructions for two or three either made by Atlas or made by Royal for Atlas lever operated closers. I knew that Precision (and a lot of others) made 3AT and several other type collets but I didn't know that they also made a closer. To install all of the ones for Atlas, you removed the threaded collar that sets the spindle bearing preload and screw the closer assembly on in its place. Other makes may have had a longer spindle. But in any case, compare what you have to the exploded view parts list drawings of the Atlas ones and you may be able to figure out what's missing from yours.
Or post photos of what you have.