That 4 wire connector is only going to provide for your lights
; tail, turn, brake and emergency flashers. For a complete hookup, you will have to go to a 7 wire connector, which will allow you to hook up your 12v hot for the trailer, brake controller and if you need, back up lights
. If you don't have brakes
, you will at least have to run a wire from the battery to the correct pin on the 7 wire. This line should have a circuit breaker in it and be sized properly to reduce voltage drop from the battery to the trailer, say 10 gauge or so.
Of course you will have to wire the trailer for 7 wire as well.
As to the vehicle side, there are some 7 wire connectors which you can plug into the 4 wire connector, simplifying installation.
For more information you can try here: