PhD supervisor (who I use as a reference) is the department director for position I am applying for. Should this bias be avoided? I am applying for a position at a University. The director of the department at the University I am applying to was my PhD supervisor.
Is it still proper to ask them to provide a letter of recommendation? Or is this a bias (conflict of interest) I should try and avoid?
EDIT: The director IS involved with both the interviewing and hiring process; however, they said to still use them as a reference.
I suggest that you ask the person whether they believe it is proper for them to write you a letter. They know the institution to which you are applying and its procedures. If they indicate that it should be fine, then it is fine. Otherwise, look elsewhere for a letter.
But it is good to avoid assumptions in a case like this. The director may be involved or not. A letter from them might be considered proper or not. Don't assume. Don't guess. Ask.
You can indicate in your note that you don't know the proper rules and, while you would value a letter, you will understand if they think it improper. Hopefully you know them well enough that such a note won't seem out of order to them.