Fusing a low-resolution hyperspectral image (HSI) with a high-resolution (HR) multi-spectral image has provided an effective way for HSI super-resolution (SR). The key lies on inferring the posteriori of the latent (i.e., HR) HSI using an appropriate image prior and the likelihood determined by the degeneration between the latent HSI and the observed images. However, in scenarios with complex imaging environments and various imaging scenes, the prior of HSIs can be prohibitively complicated and the degeneration is often unknown, which causes it difficult to accurately infer the posteriori of each latent HSI. To tackle this problem, we present an unsupervised test-time adaptation learning (UTAL) framework for HSI SR under unknown degeneration. Instead of directly modeling the complicated image prior, it first implicitly learns a content-agnostic prior shared across different images through supervisedly pre-training a mutual-guiding fusion module on extensive synthetic data. Then, it adapts the shared prior to those private characteristics in the latent HSI for posteriori inference through unsupervisedly learning a self-guiding adaptation module and a degeneration estimation network on two observed images in the test phase. Such a two-stage learning scheme models the complicated image prior in a divide-and-conquer manner, which eases the modeling difficulty and improves the prior accuracy. Moreover, the unknown degeneration can be estimated properly. Both of these two advantages empower us to accurately infer the posteriori of the latent HSI, thereby increasing the generalization performance in real applications. Additionally, in order to further mitigate the over-fitting in coping with more challenging cases (e.g., degenerations in both spectral and spatial domains are unknown) and speed up, we propose to meta-train UTAL on extensive synthetic SR tasks and solve it using an alternative optimization strategy such that UTAL learns to produce good generalization performance in real challenging cases with a small number of gradient descent steps. To verify the efficacy of UTAL, we evaluate it on HSI SR tasks with different unknown degenerations as well as some other HSI restoration tasks (e.g., compressive sensing), and report strong results superior to that of existing competitors.