Hound's absolutely right. 新 (shin in our alphabet) means new. So it means New Star Trek.
I'm actually surprised they didn't follow the original Japanese name and name TNG, 新宇宙大作戦 (Shin Uchū Daisakusen) New Cosmic Operation or 宇宙大作戦次世代 (Uchū Daisakusen Jisedai) Cosmic Operation Next Generation. I'm guessing Paramount was more involved in the dubbing process and insisted on a more literal, katakana translation.
A Fairly direct translation would be something like スタートレック 次世代 (Star Trek Jisedai) which is literally Star Trek Next Generation, but I think jisedai wouldn't work in this context. You could also just write it out in Katakana like they do for all foreign words, but some of the meaning might've been lost on people in Japan during the 80's.
I'm actually surprised they didn't follow the original Japanese name and name TNG, 新宇宙大作戦 (Shin Uchū Daisakusen) New Cosmic Operation or 宇宙大作戦次世代 (Uchū Daisakusen Jisedai) Cosmic Operation Next Generation. I'm guessing Paramount was more involved in the dubbing process and insisted on a more literal, katakana translation.
A Fairly direct translation would be something like スタートレック 次世代 (Star Trek Jisedai) which is literally Star Trek Next Generation, but I think jisedai wouldn't work in this context. You could also just write it out in Katakana like they do for all foreign words, but some of the meaning might've been lost on people in Japan during the 80's.