Should I remove my slower RAM sticks to let the faster ones run at full speed?

Check what that 1666 reading actually represents before pulling anything. DDR means double data rate, so a memory clock of 1666 MHz corresponds to about 3333 MT/s, not 1666 MT/s. A 3200-rated kit normally runs at a 1600 MHz memory clock.

Look at the labels on both kits and check the current memory clock or data rate in a monitoring tool or BIOS. If the reading is the clock, your RAM may already be running faster than you think. If it's the effective data rate, that's a different situation.

Try both configurations and measure. Run the games or workloads you care about with all 24GB, then with just the 16GB kit. Check the actual speed each time, since removing sticks won't automatically guarantee the 3200 profile is enabled.

Pay attention to memory usage and stuttering, not just average frame rates. The faster 16GB setup may do better when it has enough capacity, but running short of RAM can make the extra 8GB more valuable than the speed difference.

The two kits are generally going to run at a common speed and timings, so a slower kit can hold the faster one back. That doesn't mean the older sticks are necessarily the cause here, though. Four sticks can also be harder on memory stability than two, and the actual settings matter.

If you test the 16GB kit alone, check your motherboard manual for the recommended two-stick slots. Then enable its rated memory profile in the BIOS if needed and test for stability. The rated speed isn't guaranteed with every combination of parts.

Double-check the old sticks' labels. DDR3 and DDR4 aren't interchangeable in normal motherboard slots, so if they're installed and working alongside the 3200 kit, don't assume the 1666 figure means they're DDR3. It could be a clock reading or a mistaken speed.