I have a trademark for John. Do I have priority over others in registering John.art domain?

Not necessarily.

Between December 2016 and February 2017 the .art registry ran an ICANN-mandated registration phase called the “Sunrise period” where trademark holders who had registered their trademarks with ICANN’s Trademark Clearinghouse had priority to register their domains in advance of the general public. In General Availability, domains are now registered on a first-come-first served basis. Therefore, having a trademark does not give priority on the registration. If another party has registered your trademarked name, you might have remedies at your disposal (described below in the FAQs).