(idiomatic) To telephone, to call someone on the telephone.(verb)
To enter a payment into a cash register, or till in a shop.(verb)
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Use "ring up" in a sentence
"He gave some instructions to Janvier and went off in a taxi to the Quai des Orfèvres, where he found a message asking him to ring up Dr Paul, the official pathologist."
"She had been found by a couple corning from the other end of the block who had been having a late snack in the Golden Egg. The woman had had to be sedated and taken to hospital; her husband had just managed to ring up the police before he got sick all over the telephone kiosk."
"By the time that I reached home I had decided that I'd ring up Stenning and see if he could come."