The only real way to know if it will work is to try it. Nobody can tell you for sure if it will work. The worst that will happen is either it will be forced to run at the JEDEC standard of 2133 or it won't work at all. You should try to find a second module that is as close to the original as possible or your best bet is buy a 2x4GB kit instead and keep the original module as backup.
You also don't have to get the same speed ram to mix modules and often a faster module with lower cas latency (CL) will have a better chance of working with a lower end original module with worse high cas latency. So for example if you got a 2666 CL17 module to mix with your current 2400 CL17 module, they would be more likely to function together without a problem, but that is not a guarantee they will work at all. If you have the money to spare, get a 2x4GB kit instead.