'exercise competence' is correct and can be used in written English.
You can use it to express the idea that someone is capable or has the necessary skills or knowledge to do something, especially if it is something complex or difficult. For example: "The engineer was required to exercise competence in order to find a solution to the complex problem."
But in saying that, "Where the Union has not exercised or ceases to exercise its competence in an area of shared competence, the member states may exercise theirs," it seems to be saying, to Eurosceptic ears, that national governments will only be free to act in these areas when the Union chooses not to.
There is no option to decline to exercise Community competence, and neither the Council, the Commission nor Parliament has the power to waive these Community competences.
This lists a series of policy areas where European nations "may" legislate, but only when "the Union has not exercised or ceases to exercise its competence".
In other words, attempting to exercise normative competence (that is, to promote autonomy) relative to the prevailing norms entails adopting a set of norms that is oppressive to oneself.
Thus, the focus of this work is a system where activities are designed in order to exercise each competence to some extent and assess them according to their degree of acquisition.
The Parliament may exercise its competence... until the end of the second regular session of the parliamentary term commencing after the offence was committed.
More emphasis on the prerequisites and possibilities for psychiatrists to gain, maintain, and optimally exercise professional competence in insurance medicine, in the context in which they work, is warranted.
That said, it is also the case that this flexibility will allow the Member States to enjoy, where the Community does not exercise its competence, an institutional framework to help citizens gain access to justice in third countries, especially in the area of family rights.
Any woman of accomplishment becomes more acceptable if she can be seen as pursuing her ambitions, exercising her competence, in a feminine (wily, non-confrontational) way.
