To get the zsh shell to perform command substitution on the value of PS1, set the PROMPT_SUBST shell option:

set -o PROMPT_SUBST
PS1='$(pwd) > '

Note that there is no need to export the PS1 variable.

For more information about this, see the "EXPANSION OF PROMPT SEQUENCES" section in the zshmisc manual on your system.

When you use

PS1="$(pwd) > "

the value given to the PS1 variable is expanded before the assignment takes place. This is why it does not change when you change directories.

To get the zsh shell to perform command substitution on the value of PS1, set the PROMPT_SUBST shell option:

set -o PROMPT_SUBST
PS1='$(pwd) > '

Note that there is no need to export the PS1 variable.

The reason why the PROMPT_SUBST shell option is not set by default is likely that the zsh shell already has rich syntax for prompt expansions.

Your example could, for instance, be replaced by

PS1='%/ > '

For more information about this, see the "EXPANSION OF PROMPT SEQUENCES" section in the zshmisc manual on your system.

When you use

PS1="$(pwd) > "

the value given to the PS1 variable is expanded before the assignment takes place. This is why it does not change when you change directories.