Although Terrier is the most recently written of the Tortall books, chronologically it is the first. Rebakah "Beka” Cooper (the six-times-great-grandmother of George Cooper, from The Song of the Lioness quartet and later books) is a trainee Dog – the slang term for members of the Provost's Guard, and it is her job to patrol the streets of the worst parts of Corus and make sure justice is done.
Beka follows in the tradition of the other Tortall heroines (or perhaps, startis the tradition of Tortall heroines): she is strong, but not without weaknesses; she is clever, but still has much to learn; she is conscious of her duty, and is keen to help – indeed, she will go to great lengths in order to do that.
However there are several things that separate Terrier from previous Tortall novels. Not only is Terrier written in first person, it is written in diary format, with Beka marking out the days and times, and providing her own personal spin on describing things. There's even a giant black splotch on the second half of one page where the ink she uses to write was spilled.
Terrier also marks a departure from the world of nobles and nobility in which the previous series are set (even though Daine of The Immortals is common-born, a good chunk of the cast are nobles, and the storyline involves the nobility), and instead we find ourselves back in the Lower City, albeit two centuries earlier. The Court of the Rogue, which features in Song of the Lioness, makes a return, as does the seedy side of Corus life. Only this time we see more of it: from prostitution to murder to threats of rape, Terrier is much more adult than previous Tamora Pierce books.
If you're a fan of Tamora Pierce, tough heroines or fantasy, then pick up Terrier. Just note that it is grittier and down and dirty than other series, so if that doesn't sound right to you, try one of Pierce's other Tortall series first.