Yes. God says he will not have pity on Israel, but he will have pity on the house of Judah and save them by the LORD their God Hosea 1:6–7. The verse contrasts Israel’s judgment with Judah’s rescue.
In Hosea 1:6–7, Hosea’s next child is given a name that signals a turning point: Israel will no longer receive the same compassion and “letting it go” as before. Yet the message is not identical for everyone. Judah is singled out for mercy and for a kind of rescue that does not depend on normal military means. These verses sit inside the opening sign-act narrative where Hosea’s family becomes a public message.
Hosea 1:6–7 continues the opening sign-act: a real child is born, and her name carries a public message. The name “Look-ruhamah” signals a change in how Yahweh will treat the “house of Israel”: the text explicitly says mercy will no longer be shown, and that Yahweh will not keep “pardoning” as before. The passage also makes an explicit contrast.
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with Hosea 1:6-7, then read the surrounding section so the answer stays connected to the passage's flow.
6She conceived again, and bore a daughter. [Yahweh] said to him, Call her name Look-ruhamah; for I will no more have mercy on the house of Israel, that I should in any wise pardon them.
7But I will have mercy on the house of Judah, and will save them by Yahweh their God, and will not save them by bow, nor by sword, nor by battle, by horses, nor by horsemen.