How can I reach out to a big director for a job I want in her department?

So, I worked for X company 3 years ago and left to get a masters and a fellowship. I met a director for X company before I left in 2016 and this past March 2019 when I went to an event for Alumni for the fellowship program.

I did mention to her in passing that I would like to come back but at that time they weren't hiring. but she did say "we would love to have you back" although she seemed not as enthused

anyways..I saw her department is doing ALOT of hiring now, about 7 positions of which I could qualify for 3-4. She obviously would not be the point of contact as her day to day doesn't include hiring, and she's the director of the department and the team lead would eventually do the interviewing and hiring etc.

Can I reach out to her? and how? Can anyone give me some formats I can use?

thank you.

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