Job decision is stressing me out.

Hello all! So I had been looking for a full time library position for over a year now and finally acquired one recently. I resigned from my part time position at my library and the day after, the director let me know that they would really like to keep me (for Spanish programming) and she finally got a full time position made for me and would like me to apply. I would really love to stay with them and continue doing the programming but I also don’t want to let this new job down either. How do I gently let the new job know about my decision to leave so soon if I get it? I’m so stressed and feel so bad. This will be my first week with them.

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