What does the field "Prohibited Elements" in the plugin settings of TinyMCE (is at the very bottom of the 1st tab) contain?

If it contains "script", remove that, and it will work.

Sure I tried that, and it's allows me only to add a <script></script> tag, but I need to add an attribute onclick="" to an existing tag.
TinyMCE just deletes all event attributes like onclick at any settings, that's the problem.

Hmm, I see ... sorry for asking.

Kein Problem!
Yes, try to play with this. Judging by deep googling this is the old issue but there is no solution for now.
At least I have not found it yet.

Have you looked through the tinymce bug tracker?

What is the tag that you are trying to put the onclick? <a> or something else?

Also from tinymce' documentation:

Also note that all event attributes are excluded by default since it's a bad practice to use inline script handles like "onclick". You can manually add extra elements and attributes using the extended_valid_elements option.

https://www.tinymce.com/docs/configure/content-filtering/#extended_valid_elements

dgt41, I tried to add onclick to different tags.
Many thanks for link!
Now topic can be closed, the problem is solved.
I just set *[*] value for the 'Valid Elements' field, according to to the TinyMCE documentation:

Use *[*] to include all elements and all attributes.

https://www.tinymce.com/docs/configure/content-filtering/#specialvariables

Closed as requested - this is a tinymce issue not one we can alter