Hyphens, En Dashes, Em Dashes

Q. Now here’s one phrase I’ve always found difficult to hyphenate. “Foreign policy making elite,” referring to an elite making foreign policy. Would Chicago write “foreign policymaking elite”?

A. Write “foreign-policy-making elite.” See CMOS 6.80 for some analogous examples.

[This answer relies on the 17th edition of CMOS (2017) unless otherwise noted.]