Answer: PLAYPHONETAG

"Playing phone tag" refers to a situation where two or more people repeatedly miss each other's phone calls, resulting in a back-and-forth exchange of voicemails or missed calls. It can be a playful term to describe the frustration of trying to have a phone conversation when each person is constantly missing the other's call. The clue "Exchange rings" likely refers to the act of making phone calls, as traditionally when a phone call is made, the phone rings on both ends as an indication of the call.

Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: Exchange rings?. Explanations are generated by AI and may be inaccurate.