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The `preexec` function is called right before executing commands, so it's the place to do this sorta things.

This solution is adapted from [Dan Berindei's](https://stackoverflow.com/users/55870/dan-berindei) [original answer](https://stackoverflow.com/a/14084584/9309049) (CC BY-SA 3.0) to a related question:

```zsh
preexec () {
  TIME=`date +"[%H:%M:%S]"`
  C=$(($COLUMNS-12))
  echo -e "\033[1A\033[${C}C ${TIME} "
}
```
Just paste it in your `.zshrc` file.

It uses [ANSI excape codes](https://en.wikipedia.org/wiki/ANSI_escape_code) to print the timestamp to the previous line (prompt line). Note that you will likely need to modify the columns count if you change the timestamp format.