Wiktionary
n. (context idiomatic English) A situation in which a person unsuccessfully attempts to contact another person by telephone and leaves a message instead, and in which the second person then unsuccessfully attempts to return the initial call and leaves a message for the first person, and so on as if the two are playing a game of tag in which the most recent person to have been left with a message is now designated as "it" (i.e. as the player now obliged to chase the other and to attempt anew to make contact).
Usage examples of "telephone tag".
After all that, she didn't tell me the name of the book, and now I'll have to call her back, and we'll probably play telephone tag for a week.
Aaron dialed the number in Oakland, steeling himself for a lengthy round of telephone tag.
We're playing telephone tag, but when we hook up, I'll say something.
It seemed a better option than playing telephone tag for the next two days.
OPERATING FROM A SUITE at the Hay-Adams Hotel, Stephano spent the morning playing telephone tag with harried corporate executives.