Ygor's solution will work with ksh95 or pdksh. But ksh88 only expands variables...it won't do a general parse. I am not real fond of invoking the date command with each each display of the prompt.

ksh95 has a feature called discipline functions and these can be used to create dynamic variables that work like RANDOM.

Here is a solution that will work with all three versions of ksh. If we set SECONDS, it will continue to advance. So if we set it to the number of seconds since midnight it will serve as a time-of-day clock. To get from seconds-after-midnight to hours:minutes:seconds we need to do some arithmetic. If we reference a imaginary array, we can compute a subscript for it and use side effects from the subscript computation to set other variables. A single date process is used to initialize the clock, but after that the time is computed by the shell itself.

unset _h _m _s
eval $(date "+_h=%H ;_m=%M ;_s=%S")
((SECONDS = 3600*${_h#0}+60*${_m#0}+${_s#0}))
typeset -Z2 _h _m _s
_tsub="(_m=(SECONDS/60%60)) == (_h=(SECONDS/3600%24)) + (_s=(SECONDS%60))"
_timehm='${_x[_tsub]}$_h:${_m}'
_timehms='${_x[_tsub]}$_h:$_m:${_s}'

PS1="$_timehm $ "