How to recreate a SQL Server audit without an audit gap?
I want to reapply the audit and audit spec definition every evening in case the DBAs change it


Engaging in an arms race against the rightful admins is only going to cause delay and confusion. 


Explain to DBAs the role and purpose of the audit, ask them not to change it
Use the audit itself to detect tampering
Follow up upon detecting tampering with administrativia to get the responsible party questioned/rewarded/punished depending on situation


If you cannot enforce above, it means by definition that you are not be able to enforce an audit, so why bother?

As for specifically the question, this advice applies always, to any situation: do not blindly re-apply a template 'in case it changed', only apply it if it had changed.

Ask your DBAs to help you, do not ask us to help you against your DBAs.