user10820: In Adobe Premiere there are shortcut keys to play a clip right from the In mark to Out mark. Shortcut on a PC  is Ctrl + Shift + Space. 
However, how can I play a clip only till my Out mark? Not my full selection from In to Out, but from an arbitrary point of a selection only to my Out mark? It should stop playing on my Out mark.

user6273: I don't think this is possible. Edit: Turns out I was wrong. As Green mentions, CTRL+Spacebar will do exactly what you asked for. I'll leave the rest of my answer as alternatives to that.
Another option is the Play Around Shortcut, Shift+K, which will start playback a couple of seconds before your current timemarker position and stop a couple of seconds behind it. You can customize the Preroll and Postroll seconds under Preferences → Playback.

user10820: To "Play from Playhead to Out Point":

PC: Ctrl + Spacebar
Mac: Ctrl + Spacebar

To "Play In to Out": 

PC: Ctrl + Shift + Spacebar
Mac: Opt + K

from: https://helpx.adobe.com/premiere-pro/using/keyboard-shortcuts.html

10820: <p>In Adobe Premiere there are shortcut keys to play a clip right from the <strong>In mark to Out mark</strong>. Shortcut on a PC  is <kbd>Ctrl</kbd> + <kbd>Shift</kbd> + <kbd>Space</kbd>. </p>

<p><strong>However, how can I play a clip only till my Out mark?</strong> Not my full selection from In to Out, but from an arbitrary point of a selection only to my Out mark? It should stop playing on my Out mark.</p>
 6273: <p>I don't think this is possible. <strong>Edit:</strong> Turns out I was wrong. As Green mentions, <kbd>CTRL</kbd>+<kbd>Spacebar</kbd> will do exactly what you asked for. I'll leave the rest of my answer as alternatives to that.</p>

<p>Another option is the <strong>Play Around</strong> Shortcut, <kbd>Shift</kbd>+<kbd>K</kbd>, which will start playback a couple of seconds before your current timemarker position and stop a couple of seconds behind it. You can customize the <strong>Preroll</strong> and <strong>Postroll seconds</strong> under <strong>Preferences</strong> → <strong>Playback</strong>.</p>
 10820: <p>To "Play from Playhead to Out Point":</p>

<ul>
<li>PC: <kbd>Ctrl</kbd> + <kbd>Spacebar</kbd></li>
<li>Mac: <kbd>Ctrl</kbd> + <kbd>Spacebar</kbd></li>
</ul>

<p>To "Play In to Out": </p>

<ul>
<li>PC: <kbd>Ctrl</kbd> + <kbd>Shift</kbd> + <kbd>Spacebar</kbd></li>
<li>Mac: <kbd>Opt</kbd> + <kbd>K</kbd></li>
</ul>

<p>from: <a href="https://helpx.adobe.com/premiere-pro/using/keyboard-shortcuts.html" rel="nofollow noreferrer">https://helpx.adobe.com/premiere-pro/using/keyboard-shortcuts.html</a></p>
