I'm applying for tenure-track teaching positions right now and have, more or less, a single cover letter that I modify for each one of my applications.
It so happens that the department my advisor teaches in has such a position and I am intending to apply. To give some context to this, my graduate program was at an institution that is associated to but very distinct from the institution my advisor is a faculty member of. Though my PhD advisor is one of my biggest professional connections, I hardly have any other connections within this department, though most other people there know that I was her PhD student and would certainly recognize my name from my application.
My question is: Is it necessary/recommended that I modify my cover letter to reflect my relationship with my advisor in any way? If so, what should be included?
I honestly think there is a slim chance I would be selected for an interview let alone hired, but I would like to get a sense of what's appropriate in this kind of situation.