A victor gives no quarter when the victor shows no clemency or mercy and refuses to spare the life in return for the surrender at discretion (unconditional surrender) of a vanquished opponent.

Under the laws of war

Laws of war

The law of war is a body of law concerning acceptable justifications to engage in war and the limits to acceptable wartime conduct...

  "... it is especially forbidden ... to declare that no quarter will be given". This was established under Article 23 of the IV Convention – The Laws and Customs of War on Land of the Hague Conventions of 1907

Hague Conventions (1899 and 1907)

The Hague Conventions were two international treaties negotiated at international peace conferences at The Hague in the Netherlands: The First Hague Conference in 1899 and the Second Hague Conference in 1907...

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Since a judgment on the law relating to war crimes and crimes against humanity at the Nuremberg Trials

Nuremberg Trials

The Nuremberg Trials were a series of military tribunals, held by the victorious Allied forces of World War II, most notable for the prosecution of prominent members of the political, military, and economic leadership of the defeated Nazi Germany....

 in October 1946, the 1907 Hague conventions, including the explicit prohibition to declare that no quarter will be given, are considered to be part of the customary laws of war and are binding on all parties in an international armed conflict.

Etymology

The term originates from an order by the commander of a victorious army that they "will not quarter (house)" captured enemy soldiers. Therefore, none can be taken prisoner and all enemy combatants must be killed. A second derivation given equal prominence in the Oxford English Dictionary

Oxford English Dictionary

The Oxford English Dictionary , published by the Oxford University Press, is the self-styled premier dictionary of the English language. Two fully bound print editions of the OED have been published under its current name, in 1928 and 1989. The first edition was published in twelve volumes , and...

 (OED) is that quarter (n.17) can mean "Relations with, or conduct towards, another" as in Shakespeare Oth. II. iii. 180, "Friends all..In Quarter, and in termes like Bride, and Groome." So "no quarter" may also mean to refuse to enter in to an agreement (relations) with an enemy attempting to surrender. The OED mentions a third possible derivation but says "The assertion of De Brieux (1672 Origines..de plusieurs façons de parler, 16) that it arose in an agreement between the Dutch and Spaniards, by which the ransom of an officer or private was to be a quarter of his pay, is at variance with the constant sense of the phrases give and receive quarter."

See also

• List of established military terms
• Ordinance of no quarter to the Irish
  Ordinance of no quarter to the Irish
  The Ordinance of no quarter to the Irish was a decree of the English Long Parliament passed on 24 October 1644 in response to the Irish Confederation of Kilkenny threat to send troops from Ireland to support King Charles I during the English Civil War that ordered Parliamentary officers to give no...
  
  
• El Degüello
  El Degüello
  El Degüello is a bugle call, notable in the US for its use as a march by Mexican Army buglers during the 1836 Siege and Battle of the Alamo. "Toque a Degüello" was introduced to the Americas by the Spanish armies and was later adopted by the patriot armies fighting against them during the Spanish...
  
  
• Clemencia para los vencidos
  Battle of Las Piedras
  The Battle of Las Piedras was fought on May 18, 1811 as part of the Uruguayan struggle for independence.-Background and development of events:...