You build up staff morale ,yet every time your director speaks to them he\she discourages staff as he\ she has no people skills. How do you handle this?

First we should figure out the reason behind his behavior, sometimes these directors do that because they feel under-qualified or fear losing their jobs so discouraging you make them feel better about them selves.
Then we should learn and adapt to the director's preferred communication style.
Stay positive.
Find what develops trust.
Build autonomy based on trust.
Finally, Stay under the radar, now you're off and running, you have your boss's trust and growing autonomy, the key now is to establish boundaries that will keep you happy and fulfilled without triggering a backlash from your toxic director.

Thank you Salah,excellent advise.