The ESP Guitar Company

(Sorry for the pictures messing up the post.)

In short, you have the wrong arm for your trem. It appears to be for an Ibanez trem system.

The trem arm you need is the screw-in variety. 

Here is a Floyd Rose Special assembly arm. https://www.guitarcenter.com/Floyd-Rose/Special-Tremolo-Arm-Black-1356368700650.gc?cntry=us&source=4WWMWXGP&gclid=Cj0KCQiA4uCcBhDdARIsAH5jyUkBnuXcDkIj9lYkQt7-ebh7NQxE1zq2j7vzhNh1ykjLDrc5OHG3g_waAhtQEALw_wcB

You can use this opportunity to upgrade entire the trem arm system to a Floyd Rose Original Arm, the Turbo Trem Arm (which has an allen key at the bottom so you tighten or loosen nuts - quite handy), or buy the Floyd Rose push-in style arm assembly.

I advise the buy the entire assembly, because, if the bushings new arm don't match with those of the original, you can replace the whole system. 

Good luck.

Thanks for the reply. It's a friend's guitar I'm considering buying, in very good shape except for the arm problem.

So what you're suggesting is changing the whole floyd bridge system to an original one? Because this licensed one is of bad quality? A new arm is affordable, but the whole system would not be worth it for me since I can buy it as it is for a relatively cheap price. If this floyd is of lesser quality and the owner can't find the original arm I would rather consider other guitars.

The licensed Floyd is pretty reasonable. There's no reason to swap it out unless you do a bunch of trem work as part of your playing. The link that Thrash gave will work for you. It's around $15 depending on where in the world you live.

I don't do a lot of trem work except sometimes in solos, but when it happens it could get "violent". So if it gets easily out of tune in such situations, I'm not sure...

Work with it for a while. If after a few weeks/months you're not happy with the tuning stability, consider upgrading the trem.

Is it expensive to upgrade the trem for a fee? getting over it