I have no backlog but my marksheet was delayed; will this cause any problem for my application in New Zealand?

A delayed marksheet usually won't cause major issues with your application, especially since you have no backlogs.

Most New Zealand universities accept provisional or interim transcripts to start the application process. You can submit your final official marksheet once it becomes available. However, you must provide all required documents as soon as you receive them, as universities may request interim results or provisional certificates to assess your application.