There is nothing to measure by anymore.
One won't be able to even define what Time is.
It simply vanishes and ceases to exist.
There's no such thing as "time" anymore.
But interestingly enough, its close cousin, namely Space, would still be around, live but maybe not kicking much.
Then in the absolute stillness of the night, with one puff from Puff the Magic Dragon who just woke up, molecules and along with which everything else start moving, and bingo, Time returns, and the Sun rises.
And then Time and Space together would continue to intermingle and play and fool around like from the very start of the universe.