How to ask an university for application selection result before accepting an offer from another university?
A related, but not truly duplicate, answer

Just ask. Tell them you have been accept at X, but Y is your first choice. The admissions committee does not need much explanation since it happens all the time. Asking to speed up the process will not hurt your chances. They may not be able to speed anything up, but if they do/don't, they will not hold it against you.