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No, they've never appeared together on-screen before.

The first character mentioned in the question has appeared in the following episodes:

• Terror of the Autons
• The Mind of Evil
• The Claws of Axos
• Colony in Space
• The Daemons
• The Sea Devils
• The Time Monster
• Frontier in Space
• The Deadly Assassin
• The Keeper of Traken
• Logopolis
• Castrovalva
• Time-Flight
• The King's Demons
• The Five Doctors
• Planet of Fire
• The Caves of Androzani (as a hallucination)
• The Mark of the Rani
• The Ultimate Foe
• Survival
• The TV movie
• Utopia/The Sound of Drums/Last of the Time Lords
• The End of Time

• Most episodes of series 8, as Missy

• The Magician's Apprentice

The second has appeared in the following:

• Genesis of the Daleks
• Destiny of the Daleks
• Logopolis (as a hallucination)¹
• Resurrection of the Daleks
• Revelation of the Daleks
• Rememberance of the Daleks
• The Stolen Earth/Journey's End
• The Magicians's Apprentice

As you can see, there are only two episodes common to both characters: The Magician's Apprentice, which is the episode under consideration, and Logopolis. However, one of our two characters only appeared as a hallucination of the Doctor, and didn't share any screen time with the other.

Although I'm not excessively familiar with the Doctor Who expanded universe (by which I mean the various novel series, comics, and audio productions), a quick skim of the two characters' pages on the TARDIS Data Core (the Doctor Who wikia) indicate that they haven't met in any of them, either.

¹ Hat tip to Elliott Frisch for reminding me of this in comments

No, they've never appeared together on-screen before.

The first character mentioned in the question has appeared in the following episodes:

• Terror of the Autons
• The Mind of Evil
• The Claws of Axos
• Colony in Space
• The Daemons
• The Sea Devils
• The Time Monster
• Frontier in Space
• The Deadly Assassin
• The Keeper of Traken
• Logopolis
• Castrovalva
• Time-Flight
• The King's Demons
• The Five Doctors
• Planet of Fire
• The Caves of Androzani (as a hallucination)
• The Mark of the Rani
• The Ultimate Foe
• Survival
• The TV movie
• Utopia/The Sound of Drums/Last of the Time Lords
• The End of Time

• Most episodes of series 8, as Missy

• The Magician's Apprentice

The second has appeared in the following:

• Genesis of the Daleks
• Destiny of the Daleks
• Logopolis (as a hallucination)¹
• Resurrection of the Daleks
• Revelation of the Daleks
• Rememberance of the Daleks
• The Stolen Earth/Journey's End
• The Magician's Apprentice

As you can see, there are only two episodes common to both characters: The Magician's Apprentice, which is the episode under consideration, and Logopolis. However, one of our two characters only appeared as a hallucination of the Doctor, and didn't share any screen time with the other.

Although I'm not excessively familiar with the Doctor Who expanded universe (by which I mean the various novel series, comics, and audio productions), a quick skim of the two characters' pages on the TARDIS Data Core (the Doctor Who wikia) indicate that they haven't met in any of them, either.

¹ Hat tip to Elliott Frisch for reminding me of this in comments

No, Davros and the Master have never appeared together on-screen before.

Davros has appeared in:

• Genesis of the Daleks
• Destiny of the Daleks
• Logopolis (as a hallucination)¹
• Resurrection of the Daleks
• Revelation of the Daleks
• Rememberance of the Daleks
• The Stolen Earth/Journey's End

• The Magicians's Apprentice

The Master has appeared in:

• Terror of the Autons
• The Mind of Evil
• The Claws of Axos
• Colony in Space
• The Daemons
• The Sea Devils
• The Time Monster
• Frontier in Space
• The Deadly Assassin
• The Keeper of Traken
• Logopolis
• Castrovalva
• Time-Flight
• The King's Demons
• The Five Doctors
• Planet of Fire
• The Caves of Androzani (as a hallucination)
• The Mark of the Rani
• The Ultimate Foe
• Survival
• The TV movie
• Utopia/The Sound of Drums/Last of the Time Lords
• The End of Time

• Most episodes of series 8, as Missy

• The Magician's Apprentice

There are only two episodes where both Davros and the Master appeared; the first is the one under discussion. The other is Logopolis, but Davros only appeared in that episode as a flashack/hallucination, and never encountered the Master.

¹ Hat tip to Elliott Frisch for reminding me of this in comments

No, they've never appeared together on-screen before.

The first character mentioned in the question has appeared in the following episodes:

• Terror of the Autons
• The Mind of Evil
• The Claws of Axos
• Colony in Space
• The Daemons
• The Sea Devils
• The Time Monster
• Frontier in Space
• The Deadly Assassin
• The Keeper of Traken
• Logopolis
• Castrovalva
• Time-Flight
• The King's Demons
• The Five Doctors
• Planet of Fire
• The Caves of Androzani (as a hallucination)
• The Mark of the Rani
• The Ultimate Foe
• Survival
• The TV movie
• Utopia/The Sound of Drums/Last of the Time Lords
• The End of Time

• Most episodes of series 8, as Missy

• The Magician's Apprentice

The second has appeared in the following:

• Genesis of the Daleks
• Destiny of the Daleks
• Logopolis (as a hallucination)¹
• Resurrection of the Daleks
• Revelation of the Daleks
• Rememberance of the Daleks
• The Stolen Earth/Journey's End
• The Magicians's Apprentice

As you can see, there are only two episodes common to both characters: The Magician's Apprentice, which is the episode under consideration, and Logopolis. However, one of our two characters only appeared as a hallucination of the Doctor, and didn't share any screen time with the other.

Although I'm not excessively familiar with the Doctor Who expanded universe (by which I mean the various novel series, comics, and audio productions), a quick skim of the two characters' pages on the TARDIS Data Core (the Doctor Who wikia) indicate that they haven't met in any of them, either.

¹ Hat tip to Elliott Frisch for reminding me of this in comments

No, Davros and the Master have never appeared together on-screen before.

Davros has appeared in:

• Genesis of the Daleks
• Destiny of the Daleks
• Resurrection of the Daleks
• Revelation of the Daleks
• Rememberance of the Daleks
• The Stolen Earth/Journey's End

• The Magicians's Apprentice

The Master has appeared in:

• Terror of the Autons
• The Mind of Evil
• The Claws of Axos
• Colony in Space
• The Daemons
• The Sea Devils
• The Time Monster
• Frontier in Space
• The Deadly Assassin
• The Keeper of Traken
• Logopolis
• Castrovalva
• Time-Flight
• The King's Demons
• The Five Doctors
• Planet of Fire
• The Caves of Androzani (as a hallucination)
• The Mark of the Rani
• The Ultimate Foe
• Survival
• The TV movie
• Utopia/The Sound of Drums/Last of the Time Lords
• The End of Time

• Most episodes of series 8, as Missy

• The Magician's Apprentice

No, Davros and the Master have never appeared together on-screen before.

Davros has appeared in:

• Genesis of the Daleks
• Destiny of the Daleks
• Logopolis (as a hallucination)¹
• Resurrection of the Daleks
• Revelation of the Daleks
• Rememberance of the Daleks
• The Stolen Earth/Journey's End

• The Magicians's Apprentice

The Master has appeared in:

• Terror of the Autons
• The Mind of Evil
• The Claws of Axos
• Colony in Space
• The Daemons
• The Sea Devils
• The Time Monster
• Frontier in Space
• The Deadly Assassin
• The Keeper of Traken
• Logopolis
• Castrovalva
• Time-Flight
• The King's Demons
• The Five Doctors
• Planet of Fire
• The Caves of Androzani (as a hallucination)
• The Mark of the Rani
• The Ultimate Foe
• Survival
• The TV movie
• Utopia/The Sound of Drums/Last of the Time Lords
• The End of Time

• Most episodes of series 8, as Missy

• The Magician's Apprentice

There are only two episodes where both Davros and the Master appeared; the first is the one under discussion. The other is Logopolis, but Davros only appeared in that episode as a flashack/hallucination, and never encountered the Master.

¹ Hat tip to Elliott Frisch for reminding me of this in comments