As a former police chief I can only describe the hiring process for the department I headed although I know of other departments who use similar process. The city commissioners first of all advertise for the police chiefs position from the applications they receive the list is narrowed down to those with the best qualifications. From there you go through the interview process with the mayor, police commissioner and any other commissioners as the mayor sees fit to have on the panel. This panel then makes the final decision on who will be the next chief. The police chiefs position is an appointed position and works at the pleasure of the mayor and city council which means the mayor can fire him without cause. This doesn't happen very often, but it does happen. Is the police chief the lacky of the mayor? This depends a lot on the chief. Mayors and police commissioners like to push their weight around so you have to stand up to them. I have often been amazed by the fact that an ordinary citizen with little or no law enforcement experience and by virtue of being elected mayor or any city commissioner suddenly becomes an expert in law enforcement administration and procedures.
As for the anti-gun bent of a lot of CLEO and departments I can see where that can easily happen because when you are a cop or a CLEO you are constantly confronted with people with guns or see the results of people who got on the wrong end of a gun and you tend to develope a strong resentment towards guns in general.
I was chief under three different mayors and only one tried to run my department, needless to say, we did not get along. Fortunately, I had a good police commissioner who backed me up. I hope this helps.