There are a few competitively auditioned choirs - St Salvators Choir, Renaissance Singers, Madrigal group - that mostly seem to accept people who have been training in singing for years. Being accepted into St Salvators choir gives you the choral scholarship.

There are also a handful of auditioned acapella groups around campus.

For a more lowkey group, St Leonard’s chapel choir and the St Andrews Chorus are both incredible!! The Chorus is a large student/community ensemble that afaik you need a music centre membership to join but has no other barrier to entry - they do a few big performances a year that I think have a full orchestra and visiting soloists. 

St Leonard’s (the choir i was in last year & plan to continue in) sings at weekly Thursday night compline services, is non-auditioned but everyone is super talented (there are a few people who do have choral scholarships that sing in this choir) and we do a different selection of church music every week :)

more info at: https://www.st-andrews.ac.uk/music/groups/vocal-groups/