I am going to apply for a competitive European research grant as a postdoc. How does finding a potential mentor in department help me to get postdoc position. Does it really increase my chance to give my application a priority?
It is in general a good idea, not just for your chances but to ensure you will find a productive or at least welcoming group to work with.
The impact on your success chance I think depends on the country of choice: in some countries (e.g. Italy), postdoc calls are advertised as a public competition with a committee that should judge your CV impartially. In other countries, a professor may hire a postdoc on his personal funds and choose the candidate of his own will. In the latter case having at least some prior contact may be strictly necessary.