The phrase "to run the tap" means to turn on the water faucet and let the water flow.
Sentences with «to run the tap»
To remove from the molds, hold the mold under running tap water or dip it in a bowl of water filled halfway. (savorybitesrecipes.com)
My girls never took a bottle, but according to some of my readers, sticking the bottle under warm running tap water works just fine. (thenaptimereviewer.com)
Run a tap through the nut to clear out any powder coating in the threads so you have good metal to metal contact with your grounding bolt. (mechanics.stackexchange.com)