1) The outlet on the shower tray may come loose if you give it a half-turn or quarter -turn anti-clockwise. Throw the gunk you find in the bin, don't rinse it down the drain!
2) Run cold water into the shower tray, stick a rubber plunger over the drain-hole and exercise you plunging muscles by pressiing and lifting plunger. Scoop up gunk and throw in bin.
3). Pour drain cleaner down outlet and leave it overnight if possible. Rinse shower tray well with cold water before using.
Try suggestions in that sequence. Do not be tempted to try 2) after 3) unless you are wearing rubber gloves and goggles.
If none of these works, call plumber.