run its course
Proceed to its logical or natural conclusion, as in The doctor said the cold would probably run its course within a week. This idiom employs course in the sense of “an onward movement in a particular path.” [Second half of 1500s]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.