My boss knows that I'm aiming for a leadership role, and I think that, worst case scenario, this would be a step toward that goal.
By all means, accept the job. It seems that your boss thinks that you are an excellent candidate, and like others said, even if the program is discontinued (doesn't mean you
failed) it will look good on your resume.
The problem will now lie in talking with the former Team Leader. Honestly, I want her input. She's done this job for a couple of years at this point, and I have never taught freshman (just seniors and 7th graders). However, I don't want to give her the impression that I was brought in either as a last-ditch effort or as an attempt to reboot the program. She will find out in August at the latest, but I'd rather discuss it with her over the summer so we can meet in person and talk openly about what worked and what didn't.
Bold above -- so Teri doesn't know that you were offered the position? But you want to talk to her before she officially finds out? I'd shy away from that.
Her comments about it being a dead-end job almost sounds like sour grapes to me. Especially with the bold below . . . did she really
leave the position of her own choosing?
Thankfully, she was very forthcoming that there is a chance the program will end and that it is currently under evaluation. The change in staffing, however, is one of the things they are testing. As she put it, "Yes, I am a firm believer that good teaching makes a huge difference for students. " I'll take that as a compliment.
I agree, I would take that as a compliment, too. It sounds like the previous staffing (Teri, Team Lead) wasn't working out too well for the program. Are they changing the entire staff? Or just Teri's position?
Which brings me to gently say "Do not ask Teri for advice."
Have you ever asked Teri for advice before? Or have you achieved this offer of leadership on your own?
Instead of seeking advice from the old team lead, ask for information from those in charge (your boss and other board members.) Ask about problems concerning the program, specifically why they are thinking about discontinuing the program. What went wrong? What went right? Over the summer, talk to them about changes that you're thinking of implementing.
It sounds, to me, that you're a little bit excited about this opportunity.
Talking to Teri might change your mind on implementing a really great idea that you had. Teri: "Oh, I tried that, but it didn't work" Maybe it wasn't the idea that was wrong, maybe it was the implementation that didn't work?
Maybe Teri just isn't as good at the job as you are.