I’m a graduate student whose current major is not music. I want to study piano as my major. There are graded music exam systems such as ABRSM, which have diploma or associate certificate degrees as well. Is it better if I get an advanced certificate from one of these exam systems in order to be more easily admitted to music schools? If so, in USA which one is the best-known exam system? Thanks.
It would be best to ask the schools where you intend to apply. Their advice is the most valuable.
The music diplomas you mention from the Associated Board are recognized by the UK National Qualifications Framework. I don't know the situation in the United States. However, in my opinion it doesn't matter in this case.
In general, admissions to performance programmes come through auditions. Limited places are available, and competition can be high. The impression you make in your audition is of the first importance. If those hearing your audition were undecided between you and another applicant, I would be amazed to learn that they decided in your favour on the basis of something like an ABRSM diploma. I feel surer still that if another applicant showed greater ability and promise on the day, having LRSM after your name would not save you.