Kill a process and wait for the process to exit

No. What you can do is write a loop with kill -0 $PID. If this call fails ($? -ne 0), the process has terminated (after your normal kill):

while kill -0 $PID; do 
    sleep 1
done

(kudos to qbolec for the code)

Related:

• What does `kill -0 $pid` in a shell script do?