How to settle a divorce case in execution with ex-husband who is outside the UAE?

There is no arrest warrant, but what I know is he can come to the UAE & pay the dues.

So don't do anything, no need to close the file. Tell him that the court will not look for him, and will not ask him for anything.

The court decides if the plaintiff requests his right. If the plaintiff (which is you) does not ask for his right, the court does not do anything, and the file remains open, but without procedures.