Reddit reviews The Age of Justinian: The Circumstances of Imperial Power (Roman Imperial Biographies)

JB Bury's History of the Later Roman Empire tends to be fairly widely available, vol 1 and 2 and is a good primer for the period. I believe there are several free versions available online. Just do a quick google search.

Despite being written in the 1920s, it still holds up rather well as a reference (and I love it for his conclusions and straightforward writing style), as he focuses on the political history of the period. He also incorporates many choice selections and citations from Procopius himself, so that might save you some trouble.

BTW, JB Bury was the editor for the previous incarnations of the Cambridge Medieval History, which is also available for free. So you can use the older book series as well.

However, remember that the more recent scholarly books on that era tend to focus on the non-political history aspects of that period, so like the social, the cultural, the economic, and so forth. Bury's historiography will be a bit out of date, but the areas most likely to hold up will be in the realm of the essential political narrative.

But if you're willing to pay for amazon money on Justinian, I see this relatively recent book, The Age of Justinian most often as a standard but accessible reference.