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When this slider appear, tap on the "bell" icon to switch to Vibrate and No interruption modes, this make it easier to switch sound profiles when you are listening to music or any other media.
See this:
/t5/Xperia-Z1-Compact/Android-5-1-Lollipop-sound-mode-options-for-z1-compact/m-p/1039135#M17948
The way I see it now, priority is just silent mode with exceptions.
Priority mode is now merged with Silent mode, on the lower part of Silent mode popup you can enable "Allow Exceptions" which will give you the so-called Priority mode.
For this you can send your suggestion to Sony directly via this link:
http://support.sonymobile.com/global-en/contactUs/
And also on Smart Connect on Google Play, leave a feedback:
https://play.google.com/store/apps/details?id=com.sonyericsson.extras.liveware&hl=en
Actually priority mode is very important for me. I only accept calls in that mode and do much more things.
Finally i found solution for this for now.
I have done restore to factory settings, i had to install all applications again but finally i got my required priority mode back.
There should be some option to turn this mode ON/OFF. Because we cannot always take backup and reset phone for this option.
This worked for me two times. Waiting for some concrete solution.