The earth wire should be connected to three things.
A ground rod a couple of meters into the earth,
The cold water plumbing system, and
The ground bar inside the service panel. (Circuit breaker box)
If the earth wire is connected to the earth or grounding system of the house, that should be sufficient. (The house earth system should already be connected safely.) I would not run two separate earth systems, one for pool and one for the house. There is the possibility of different earth potential and with a wet environment it may be hazardous.