If you are comparing processors of the same generation, the answer is yes. Intel® Xeon® Processor E7-8860 and Intel® Xeon® Processor E7-8837 belong to the same family, same socket. This is possible if you are only using 1 processor in your Server board. It is always necessary to keep using the same processor model.
Now if you want to upgrade the Xeon® Processor E7-8837 with a Xeon® Processor E7-8860 v3, this is not possible. The newest version has socket type 2011, requires more energy and supports DDR4 memories.
Intel® Xeon® Processor E7-8860 v3 (40M Cache, 2.20 GHz)
Comparison chart (E7-8860 - E7-8837)