Now that the motor is electrically and mechanically connected, you're almost ready to put it into service. Ideally, that would be with a dry run first (in some applications, a dry run isn't possible).
Connect a power analyzer to the motor branch circuit. Set up a vibration analyzer on the motor. If possible, set up a second vibration analyzer on the load. Take baseline temperature readings on the load (including any couplings); an infrared gun works nicely for this purpose. If a gearbox is involved, take a minute now to check its oil level. Starting that new motor on a dry gearbox is not a good idea.
Start the motor and observe what happens. If it seems OK, continue monitoring for several minutes. Look at the waveform on your power analyzer for unacceptable power anomalies.
Next, take temperature readings on the load and compare to baseline readings. A gearbox running clean synthetic motor oil should not significantly heat up; if that box is already hot, then further investigation of it is warranted.
If you don't have power problems, excessive vibration, or load problems, the motor's ready to be put back in service. Remove all tools, close all covers, remove lockout/tagout, notify the operators, and close the disconnect switch.