Which monarch had the longest break in their reign?

Michael I of Romania was king from 20th of July 1927 until 8th of June 1930 and then was put back into power on the 6th of September 1940 resulting in an overall break of 3743 days

Thutmose III

He became pharaoh after the death of his father (probably in 1479 BC). His step mother Hatshepsut ruled in his place as a regent (since Thutmose III was only 2). Some time later (possibly 7 years) Hatshepsut named herself pharaoh and became the de facto ruler of Egypt. Hatshepsut likely remained pharaoh until her natural death (probably 1458 BC). Which gives a 21 to 14 years gap in the rule of Thutmose III.

That said, it is possible Thutmose III was a coregent through some or even all of Hatshepsut's reign.

Definitely not as long, but notable: Napoleon I and Louis XVIII

Napoleon I, Emperor of the French, was deposed on April 2nd, 1814, abdicated on the 4th, and after being exiled to Elba, returned to France in February 1815 and took power back on March 20th, 1815 (so the gap is less than a year).

It didn't last long, of course, as he abdicated (again) on June 22nd after losing the battle of Waterloo. He was exiled (again), but this time didn't return.

Of course, conversely, Louis XVIII which was made King of France on April 6th, 1814 after Napoleon's (first) abdication, fled when Napoleon came back (March 20th, 1815), was restored after Napoleon's (second and final) abdication and the short-lived and disputed reign of Napoleon II, on July 8th, 1815. Here the gap is even shorter (the period is called the "Hundred Days").

So we had, in a bit over a year:

• Napoleon
• Louis XVIII
• Napoleon again
• Louis XVIII again

Charles II of England, Scotland and Ireland, nine years.

At the time of the execution of Charles I in 1649, England had already overthrown the monarchy (taking Ireland with it), and so Charles II did not become king of England or Ireland at that time. But Scotland had not, and so he was king of Scotland from 1649 (though not crowned until January 1651) until England defeated the Scottish royalist forces in 1651. He then resumed his kingship of Scotland at the Restoration in 1660, nine years later, when he became king of England, Scotland and Ireland.

George II of Greece, 11 Years

George II of Greece was deposed in 1924 and regained the throne in 1935, so I guess that's about eleven years. He was the second cousin of Prince Philip of England and the drama of their family's chaotic royal standing in Greece is often alluded to in shows like The Crown.

Ptolemy VIII of Egypt had a break of 18 or maybe 20 years in his reign. Wikipedia is confused about how long the gap was.

The page for Ptolemy VIII says he was deposed in 164BC and restored in 144BC - gap is about 20 years.

The Pharaoh list page says he was deposed in 163BC and restored in 145BC - gap is 18 years.

Another site's king list says deposed in 163BC and restored in 145BC - also 18 years.

Another possible contender would be Gruffudd ap Cynan, King of Gwynedd four times.

He was deposed after his second reign in 1081 and imprisoned. He may have regained the throne of Gwynedd as early as 1088, though his biography claims in one place that he was imprisoned for 12 years and in another that he was imprisoned for 16 years, thus escaping and regaining power in 1093 or 1097. See the Wikipedia article on his [Escape from captivity and third reign].

https://en.wikipedia.org/wiki/Gruffudd_ap_Cynan#Escape_from_captivity_and_third_reign[1]

Unlike some of the other examples, the kings of Gwynedd ruled as well as reigned.

Some honorable mentions:

Kavad I only had a break of three years, but was definitely supposed to be forgotten after he was temporarily deposed in 496.

The Zhengtong Emperor of the Ming dynasty was deposed in 1449 after being captured by the Mongols. This reduced his value as a hostage, and he was released relatively quickly. He took the throne again seven years later after his successor had died, reigning as Tianshun emperor until 1464.

After Waldemar of Brandenburg had died in 1319, an impostor appeared in 1348 (29 years later) and succeeded in getting his title and country "back" (until 1350). Somewhat unusual for an impostor, he survived being found out and - although losing his land - was able to continue living a relatively comfortable life.

Stanisław Leszczyński was installed by Sweden as a King of Poland in 1704 and ruled until 1709 when Poland forced Sweden out. He was reelected as the king of Poland after the death of August II Mocny, in 1733 and ruled until 1736, when a Russian invasion deposed him. This gives him a respectable 27 year long break in ruling.

Poland had an elective monarchy between 1572 and 1791, with the monarch officially being elected for life, however multiple monarchs abdicated, not always of their own will, which led to this situation.

Two 5th century BC Agiad Kings of Sparta had lengthy breaks in their reigns: Pleistoanax and his son (and successor) Pausanias.

Pleistoanax - break of 19 or 20 years (reigned 458 - 446 or 445 BC, and then 426 - 409 BC)

Pausanias - break of approx. 18 years (reigned c.445 - 426 BC, and then 408 to 395 BC)

Pleistoanax, son of the regent Pausanias of Battle of Plataea fame (and later infamy), was deposed in 446 or 445 BC, supposedly for accepting a bribe from the Athenians to withdraw his army in Attica. His son, still a minor, took over and reigned for around 20 years. In 426 BC, his father was restored following 'advice' from the oracle at Delphi (this advice a result of bribery, according to Pleistoanax's opponents).

When Pleistoanax died in 409 BC, Pausanias became king again but was deposed in 395 BC for poor military leadership. He died in exile sometime after 380 BC.

Other source:

Anton Powell (ed.), 'A Companion to Sparta' (2017)

Vlad Tepes, 14 years

Vlad III first ruled as Voïvode of Vallachia for of couple of months in 1448, then from 1456 to 1462 (after a first gap of 5 and a half years), and reclaimed his throne again in late 1476, after a second gap of 14 years.

He died shortly after, but his nickname of Dracula found its way to posterity and pop culture.

This is a little stretch from your question, but Simeon II of Bulgaria ruled as

Tsar of Bulgaria from 1943 to 1946, before later serving as Prime Minister of Bulgaria from 2001 to 2005.

This is an impressive gap of 55 years, with the obvious caveat that he didn't "reclaim his throne", coming back to power as the elected prime minister of a Republic and not as a king.