The New York City Housing Authority is set to cut tenant services in the Bronx and the rest of the city.Chairman Tino Hernandez told the Daily News he plans on eliminating some services and reducing the amount of hirings for the agency. He says the moves are aimed at closing a $225 million budget gap for 2007. During recent negotiations, NYCHA sought $62 million from the state's budget. It was given $4.5 million. The organization has also tried reducing the number of its employees for the past four years and raised rent prices for the first time since 1989.