Carol, I really, really like "New Tricks"! A few years ago, I bought the complete DVD box set from AmazonUK. Now I see that Hulu is also streaming the entire series. The stories are interesting, the writing is very good, and the cast is fantastic.
I think it helps that the cast members are sort of connected in real life and have strong bonds. For instance, and I'll use the character's names, years ago, Sandra and Gerry were an item. Brian's wife on the show is Jack's wife in real life. Sandra's mother was married to the late John Thaw who was in "The Sweeney" with Gerry. Their friendships come through in their acting.
I agree that a few years in the quality of the show deteriorated somewhat. When cast members began leaving one by one, it wasn't the same. The show remains one of my all-time favorites, and I have been toying with the idea of doing a re-watch of the series.