Barclays Center is looking to hiring a small army of part-time workers for the summer. From now until June 13, the arena’s management team will be searching for applicants to fill 300 part-time positions in security and guest services. The pitch came as part of an outreach effort to residents of four community boards — 2, 3, 6 and 8 — who will be “prioritized” for the jobs, according to the center’s hiring website.  Those interested in applying must register on the Barclays job website and attend an in-person screening event in Downtown Brooklyn between now and June 13. Those selected for formal interviews will undergo a background check and drug test. Those who get a position “can expect to start working late July or August.