Your fantasy setting sounds like it is vaguely familiar to various past historical settings in Earth history.
Earth history is full of conflicts, with degrees of violence ranging from very high to vary low.
A social conflict could go on for centuries, and only have a few periods of violence, thus resulting in long periods, much longer than the time span of many stories, where there is a conflict with no violence.
I note that an election is a conflict between two parties. Efforts to gain political office are called "campaigns", just like miiitary campaigns that involve a lot of violence. But in many socities elections usually avoid violence.
And you may claim that since there weren't any elections in the past historical eras that your fantasy world is vaguely based on, there can't be any elections in your fantasy world.
But there have been elections. of various kinds, with various degrees of formality, for various political, religous, etc. positions throughout history.
For example, there have been municipal governments within andsubordinate to larger governments throughout history. Most of the Roman Empire consisted of city staes which were aristocratic republics where wealthy landowners competed to be elected as magistrates or to the city councils.
Medieval towns and cities often had local self government, and thus elections with larger or smaller electoral bodies, to elect officials.
I once read that although the governments in east Asia tended to be very despotic and absolute, the local village communities had to pay taxes, provide conscripts for the army, and not break the laws of the central goverment, but were others left to themselves by the central government. Thus each village selected its own village leadership, sometimes by some type of election process.
I note that throughout history the proportion of the population that was eligible to lect the leader varied greatly, as did the social classes, genders, and ages of the eligable voters.
Some ancient and medieval societies might have had universal suffrage for adult free males. And on the other extreme the Holy Roman Empire claimed to be the rightful government of the whole world, and for centuries the emperor was selected by the seven electors - the archbishops of Mainz,Trier, and Cologne, the King of Bohemia, the Duke of Saxony, the Count Palatine of the Rhine, and the Margrave of Brandenburg.
Christian religious leaders like abbots and bishops have often been elected by the religious and even laypersons in their jurisdictions, though they have also been appointed by higher religious and/or political leaders.
I note that there have been many periods when war, tyranny, and force have been used to convert people from one religion to another, but there have also been many peaceful missionary efforts. And even the most peaceful missionary efforts may lead to nonviolent conflicts between followers of the old and the new religions.
I note that there were scholastic institutions in the middle ages, and thus there were various nonviolent conflicts among members for leadership positions and over scholarly theories.
If someone was accused of a crime in ancient and medieval times, they might be punished violentl if convicted, being beaten, tortured, mulitlated, killed, or possibly some combination.
But in some societies there are other legal penalties, such as fines, confiscation of property, exile, etc.
A medieval Chinese pilgrim to a Buddhist kingdom in India noted that there was no death penalty there.
The Chinese emperor Xuanzong abolished the death penalty:
This was in the year 747, enacted by Emperor Xuanzong of Tang (r. 712–756). When abolishing the death penalty Xuanzong ordered his officials to refer to the nearest regulation by analogy when sentencing those found guilty of crimes for which the prescribed punishment was execution. Thus depending on the severity of the crime a punishment of severe scourging with the thick rod or of exile to the remote Lingnan region might take the place of capital punishment. However, the death penalty was restored only 12 years later in 759 in response to the An Lushan Rebellion. At this time in the Tang dynasty only the emperor had the authority to sentence criminals to execution. Under Xuanzong capital punishment was relatively infrequent, with only 24 executions in the year 730 and 58 executions in the year 736.
Beginning in about the 4th century, Japan became increasingly influenced by the Chinese judicial system, and gradually adopted a system of different punishments for different crimes, including the death penalty. However, beginning in the Nara period, cruel punishments and the death penalty were used less and less, probably as a result of the influence of Buddhist teachings, and the death penalty was abolished completely in the Heian period. The death penalty was not used for 346 years following the execution of Fujiwara no Nakanari in 810, until it was revived during the Hōgen rebellion.2
So if somone lost a political struggle for control of the imperial government, they would not be executed, mulilated, or tortured, but might be exiled from the imperial capital or suffer some other non violent punishement.
Emperor John II Komnenos who reigned from 1118 to 1143 fought many wars to defend and expand his empirie and no doubt thousands of people were killed in those wars. But:
John was famed for his piety and his remarkably mild and just reign. He is considered an exceptional example of a moral ruler, at a time when cruelty was the norm. He is reputed never to have condemned anyone to death or mutilation.
I note that in many medieval socities which did have the death penalty for various crimes, fines were used as penalties for many serious crimes.
A weregild is a defined value placed on every man graded according to rank, used as a basis of a fine/compensation for murder, disablement, injury (or certain other serious crimes) against that person. It was assessed from the guilty party, payable as restitution to the victim's family.1
The weregild was codified, for example, under Frankish Salic Code.2
Weregild payment was an important legal mechanism in early Germanic society; the other common form of legal reparation at this time was blood revenge. The payment was typically made to the family or to the clan. Similar to the way a payment was made to family, it was also a family or kin group responsibility to ensure the payment for the wrong committed, especially if the offender is unable to cover the cost of the offense himself.4
No distinction was made between murder and manslaughter until these distinctions were instituted by the re-introduction of Roman law in the 12th century.
Payment of the weregild was gradually replaced with capital punishment due to Christianization, starting around the 9th century, and almost entirely by the 12th century when weregild began to cease as a practice throughout the Holy Roman Empire.
So if two men had a personal conflict, and one tried to get the other one convicted - rightfully or wrongfully - of a serious crime, it might be a matter of life and death for the accused in many medieval societies which had the death penalty. But in many other medieval societies merely a lot of money in weregild would be at stake.
And those a afew suggestions for examples of non violent conflicts in ancient and medieval societies you might want to research to find inspiration for nonviolent conflicts in your fantasy setting.