SNMP is a way of schema-structuring information, and a protocol for (primarily) fetching that information.

Consul is a distributed database use (primarily) for informing services of the availability of other services.

Consul could have used SNMP as its data format and access protocol, but it instead uses JSON and HTTP.

If you were a masochist, you could layer SNMP on top of Consul, to expose Consul data to network management systems built on top of SNMP. Nobody does that, though, because SNMP is fundamentally obsolete, and kept relevant only by network equipment manufacturers.

The two have absolutely nothing to do with each other.