From what I can tell, I basically have the same setup as this illustration.
What I'd like to do is remove the 3-way switch on the right completely, leaving only the 3-way and 4-way switches on the left.
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To eliminate a 3-way switch, simply connect the feed wire to either one of the traveler wires, using a wirenut or similar approved connection device. Isolate the other traveler wire by capping it with a wirenut. You can identify the feed wire as it will connect to one side of the switch and the traveler wires will be on the other side. If you are not sure, in this case, it is safe to experiment: interconnect any two of the non-ground wires and isolate the other. If the circuit doesn't work, switch the isolated wire with either one of the others.
You noted that you will be replacing the switch with a switch for another circuit. One thing to watch out for is box fill. The new wires may possibly exceed the allowed fill. I'll leave it to a pro to expand on this.
Also, you may be aware of this already, but make sure to turn off the breaker for the circuit and test the wires for voltage before starting.
Yes, you can remove that 3-way switch on the right but you'll also have to change out the 4-way switch with a 3-way just to conform with standard practices. Remove from the 4-way switch the two travelers from the 3-way switch you're keeping and connect them to the two brass screws on your new 3-way that will go where your 4-way switch is now. Remove the red wire from the 4-way that goes to the 3-way you're removing and cap it with a wire nut. Remove the remaining black wire from the 4-way and connect it to the black screw on your new 3-way. At the 3-way you're removing, remove and cap the red wire and wire nut toe two black wires together. Naturally, you want to reconnect any ground wires. If you're bringing in a new circuit on a different breaker to the box where you removed the 3-way, you'll want to handle tie the breakers.