Not sure about the question, but I just edit and save the record manually

sorry, what I meant was how do I run a client script triggered from a user event script when there is an update on the record(let's say a field is updated).

Client script can not be triggered by User Event script. Client scripts require user input to trigger the events they are tied to. A Field Change or Validate Field function will not execute when the same field is updated by a User Event script since the User Event script is happening on the server side.