Is it permissible for me to act in a drama wearing Hijaab?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

A woman is not permitted to act in theater even if she wears her Hijab, since there is mixing with men and it is possible for a Muslim woman to be in seclusion with another man or he may look at her while preparing or performing a play.

Therefore, such a job diminishes a woman's modesty while she is standing and sitting in front of men.

This loss of modesty, constitutes a great loss since faith and modesty are integral.

The Prophet said: "Modesty and faith are integral (i.e. one part completes the other); if one is removed, the other part comes to an end (instantly)." [Al-Haakim and Al-Bayhaqi]
In addition, most people who take part in plays and theater are irreligious and are indifferent regarding prohibitions.

So, we advise you to fear Allaah, The Exalted, and avoid what results in mixing or that which contradicts faith and modesty.

Allaah knows best.