Sure. While most constitutional monarchies extant today have relegated the monarch to a cultural icon with purely formal and ceremonial duties, a few strong monarchies, checked but not controlled by an elected body, still exist. Examples include the Kingdoms of Bhutan and Jordan, the Emirate of Kuwait, and the principalities of Monaco and Liechtenstein. In these countries, there is an elected representative and legislative body, however the monarchy retains key practical powers in the executive and/or legislative realms of governance, including presiding over lawmaking bodies, introducing legislation, veto power, appointing key government positions, etc. The model of the American President as chief executive has led to many nations retaining a monarch with similar power, while separating the legislative and judicial powers historically united under royal control.
One does have to recognize that this state of affairs is by its very nature a compromise, and historically speaking, most monarchs that have ceded lawmaking power to an elected body have seen that body use its power to further reduce the monarch's in cultural shifts toward popular government. Of the nations that recognize a monarch as head of state, most are former British possessions that recognize Queen Elizabeth II as their formal head of state, however their governments (most of them modeled on the Westminster parliamentary system) are totally self-sufficient and separate from that of the United Kingdom, and the Queen's role in these other countries is basically a face to put on money (if that). Most of the rest are Western European nations who have seen the monarchy reduced to cultural icon status in the wake of key disagreements between the monarchy and government that forced action.
The fate of the majority of monarchies in world history as of the beginning of the 20th Century were sealed by the spread of Communism in Europe and Asia, and the counter spread of Western-style democracy (or at least initially-deferential dictatorships) by the US and NATO in Central America and Africa; by the time the tides of the Cold War receded, most royal scions of the territories involved were deposed, dead and/or in exile, and the countries adopted various versions of an elected head-of-state/head-of-government, whether parliamentary or presidential.
4See Queen Elizabeth II’s dad. – SRM – 2020-01-21T21:50:28.420
If such a person were the commander in chief of the military and nothing else, then it wouldn't be any unbearable loss to lose him in battle. He might fight at the front. If he gets splattered, his heir moves into the position. His family would receive a stipend, maybe some mansion, but he doesn't have the power to do much else (not even declare war, just fight ones declared by parliament). It's probably unwise to have him hold judicial powers (sentencing, trials) unless they're courts martial. – John O – 2020-01-21T21:55:15.097
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It is an extremely common arrangement. Victoria, Queen of the United Kingdom and Empress of India, Napoleon III, Emperor of the French, Nicholas II, Emperor and Autocrat of All the Russias, or William II, German Emperor and King of Prussia... They had extensive powers but they were not heads of government.
– AlexP – 2020-01-21T22:07:03.930Have a look at the Holy Roman Empire in some of its later years (after Charlemange and after forgot-the-name-of-the-dude was officially re-crowned by the Pope). Voltaire's quote "neither holy, nor Roman, nor an empire" was on point. The empire was a confederacy of dukes who elected an emperor. The emperor didn't have that much power over the thing - their reason for existence at one point was to coordinate the combined war efforts of the dukes from external threats, instead of each fending for themselves. Even then the emperor had to go around each duke and beg for soldiers. – VLAZ – 2020-01-21T22:07:59.157
@VLAZ: The question explicitly asks for a monarch who had "many powers", but did not do actual day-to-day governing. The Holy Roman Emperor most certainly did not have "many powers" as Holy Roman Emperor. One or another of them might have had "many powers" as King of Spain, or Archduke of Austria, or whatever was their base, but as Emperors of the HRE their powers were mostly of the soft kind. – AlexP – 2020-01-21T22:11:09.557
@AlexP true, but I wanted to point towards something slightly different, since OP didn't seem to be aware of anything between monarchs who are absolute rulers and monarchs who are a living tourist attraction. So, the emperor of the the HRE is between those - they had some powers but certainly not absolute rule. The fact that the emperor had to drag himself around and curry favours of those underneath him in order to be able to do anything is not something people associate with "emperor". So, it could be an interesting material to research and maybe partially incorporate. – VLAZ – 2020-01-21T22:18:23.577
1@VLAZ: True, and useful. And even in the modern world, very powerful presidents such as Mr. Macron of France, Mr. Putin of Russia, Mr. Erdoğan of Turkey or Mr. Xi of the People's Republic have Prime Ministers who do they day-to-day governing. – AlexP – 2020-01-21T22:26:09.730
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@AlexP there are also somewhat weird examples of a (less than a) figurehead monarch who came back into power: Simeon Saxe-Coburg-Gotha of Bulgaria was the reigning monarch of Bulgaria for a time. Political regime change booted him and the royal family and the monarchy was abolished. Decades later, after the previous regime fell, Simeon II didn't have any power as a monarch but he went into politics and became a prime minister. So...even a figurehead can still exert power in the right way.
– VLAZ – 2020-01-22T07:09:19.9901
@VLAZ: And Otto von Habsburg, who used to be crown prince of Austria-Hungary back in the day, had a late-life renaissance and was a very influential MEP (Member of the European Parliament) for two decades (1979-1999).
– AlexP – 2020-01-22T08:56:16.223Look at Sparta and their dual kingship. – Mormacil – 2020-01-29T15:37:02.600