Surah At-Taubah Ayah 4

Except those of the Mushrikin with whom you have a treaty, and who have not subsequently failed you in aught, nor have supported anyone against you. So fulfill their treaty for them until the end of their term. Surely, Allah loves those who have Taqwa (4)

Existing Peace Treaties remained valid until the End of Their Term

This is an exception regulating the longest extent of time for those who have a general treaty - with out time mentioned - to four months.

They would have four months to travel the lands in search of sanctuary for themselves wherever they wish. Those whose treaty mentioned a specifec limited term, then the longest it would extend was to the point of its agreed upon termination date. Hadiths in this regard preceeded. So anyone who had a treaty with Allah's Messenger ﷺ, it lasted until its specific termination date. However, those in this category were required to refrain from breaking the terms of the agreement with Muslims and from helping non-Muslims against Muslims. This is the type whose peace agreement with Muslims was carried out to its end. Allah encouraged honoring such peace treaties, saying,

إِنَّ اللَّهَ يُحِبُّ الْمُتَّقِينَ

(Surely, Allah loves those who have Taqwa)[9:4], who keep their promises.