"have primacy over" is correct and usable in written English.
You can use it to indicate that something has more authority or priority than something else. For example, "The local government has primacy over the federal government in this situation."
And on the Shia side of the Tigris river, militias have primacy over interior ministry or military forces.
The proposed constitution also states that European Union law will have primacy over that of member states.
Against scientific counsel otherwise, though, politicians have decided that industrial activities have primacy over the conservation needs of endangered caribou (and frankly, all things living).
Mr Nizamul's e-mail suggests that he considered Mr Ziauddin's arguments to have primacy over his own.Third, material we have seen suggests that Mr Ziauddin was communicating with the prosecution and judge about the same issues at the same time.
Isis has been pushed back from areas to the south and north of Baghdad, which are now dominated by Shia militias, who work alongside the Iraqi military and often have primacy over them.
Professional Europeans point out, for example, that Article 10 of the constitution, which states that EU law "shall have primacy over the law of the member states", is just a restatement of something that has been true since the Treaty of Rome in 1957.In this section Tidying up or tyranny?
Because hierarchical analysis revealed species had primacy over disease clustering, we focused this analysis on the most complete (murine) dataset (n=478).
There is a space for a fill or a roll at the end of a musical phrase, but the beat has primacy over the curlicues.
No one — well, maybe the boss but certainly not our peers — has primacy over, or immunity from, the needy bleat of an incoming text message.
The constitution confirmed that EU law had "primacy" over national law and gave the EU the power to sign international treaties on behalf of its member countries.
It illustrates Feigel's underlying argument that even amid the rubble the demands of personal life usually had primacy over noble projects of reconstruction.
