The phrase "in the order of precedence" is correct and usable in written English.
You can use it when talking about a hierarchy of importance for things or people, where the items at the top of the hierarchy are more important than those at the bottom. For example, "In the order of precedence, the President of the United States takes precedence over other national leaders."
Before emigrating to England, I began having these bizarre night dreams of becoming laird of the manor, with valets and maid servants bowing submissively to me, dreams that multiplied into wild fantasies of marrying into young Queen Elizabeth's family and taking my rightful place in the order of precedence.
In addition to the system for identifying loci found on master circles, there are genes found on plasmids, both linear and circular (also referred to as subgenomic circles) in the mitochondria, and these will be indicated by using a lower case letter, a z (in the order of precedence by submission to GenBank), immediately following the organellar symbol, Mt or Pt.
Members of the Order of the Bath are assigned positions in the order of precedence.
Privy Counsellors have a position in the order of precedence in England and Wales, if they have no higher one.
Reception for the medal was mixed, with veterans criticizing the placement of the medal in the order of precedence.
Members are assigned positions in the order of precedence, coming before all others of knightly rank, and above baronets.
Her own company Sally Ride Science, in its statement said clearly (note the order of precedence) - "In addition to Tam O'Shaughnessy, her partner of 27 years, Sally is survived by her mother, Joyce; her sister, Bear; her niece, Caitlin, and nephew, Whitney; her staff of 40 at Sally Ride Science; and many friends and colleagues around the country".
The guidelines deal with the order of precedence in which the Canadian flag is placed, where the flag can be used, how it is used, and what people should do to honour the flag.
