Arrow Key Up (Previous Clip) while playing

In Edit, Up and Down moves to respectively Previous and Next Clip.
When playing

- Down moves to the Next Clip
- Up moves to the beginning of current Clip.

Even typing Up twice, one cannot move past the current Clip.

I must stop playing, use Up then start playing again.
Am I doing anything wrong?

No, you're not doing anything wrong, those functions are just mislabelled.
Despite being listed as Previous Clip and Next Clip, respectively, their actual functions are (with respect to the current playhead position) Previous Edit Point and Next Edit Point. Obviously, during (forward) playback, if you try to use the 'Previous Edit Point' command to navigate the timeline you'll be fighting the actively moving playhead position. (You'll have the same problem if you playback in reverse and try to navigate with the 'Next Edit Point' command.)

I see!
How can I move to the previous clip, while playing?
Any idea?

You can use previous edit button on the player while playing to move the playhead to previous edit point, which is essentially beginning of the same clip, but as mentioned by Andy you are fighting playhead moving in opposite direction, because playhead is moving forward. Not sure what you are trying to do or why? Maybe there is a better way. What is it that you are trying to do and why?