The phrase "local parish" refers to a specific area or neighborhood within a larger community where a church is located. It represents the geographical region that the church serves. Full definition
In fact, one local parish priest here did move in his elderly mother. (religion.blogs.cnn.com)
My strong bias is toward the local, small, geographically determined local parish where people live in authentic community. (firstthings.com)
On weekends throughout 23 subsequent years, Helminiak ministered in local parishes in Baltimore, Boston, San Antonio, and Austin and, admitted to being gay in 1976. (religion.blogs.cnn.com)