Home Box Office and Paramount Pictures have extended their six-year exclusive licensing agreement, set to expire this year, for four more years, the companies said yesterday. The new deal is estimated to be worth $ 575 million.HBO pacted in ’87 for exclusive rights to Par pix, in a deal estimated to have cost the pay-cable giant around $ 500 million; that deal came at the start of what would ultimately turn into a battle with premium rival Showtime to sign exclusive agreements with the Hollywood studios. Under the new, similar deal, HBO will have access to all Paramount films released theatrically through 1997, to be telecast on HBO and Cinemax. While terms of the deal were not disclosed, the going rate for theatricals on the premium cable market has been about $ 6 million per title. Since Par has averaged 19 pictures over the last three years, the new deal would cost roughly $ 575 million; The price could go up if Par has a string of hits.