Anything I should know before...

Thats guys you've been very helpful .

Apparently, yes.  You have the advantage over any responders like myself who are unfamiliar with your turntable.  You say that some metal clips broke off, and I assume those are at the end of the cable that connects to the pins on the cartridge body.  Thus it seems likely that the other end of that cable is still OK.  If OK, you ought to be able to inspect that end and tell us and yourself where it goes, probably to the female RCA jacks you tell us about.  If so, there is your answer.
What you have to be aware of is to connect the channels correctly or else you are apt to end up with either no sound or hellacious hum, if you fail to connect ground wires properly.  The clips are generally color-coded: red, white, blue, green.
Go to this website for an explanation of the color coding of cartridge leads, and be sure to connect hot to hot and ground to ground, for right and left channels, respectively.  The task is simple, but soldering those tiny clips is often a pain in the ass even for an experienced hobbyist.
https://service.shure.com/Service/s/article/color-code-for-phono-cartridge-wiring?language=en_US

I know that one end of the cable goes to the clips on the back of the cartridge but the other end , doesn't it go connected to the rca outputs on the back of the turntable ?

All you have to do is buy new clips and solder them on. https://www.moon-audio.com/cardas-pcc-eg-cartridge-clips.html

The RCA plugs on the back of the table are for interconnects to your amplifier.