A lot will depend on what bird species your bird box is designed for. Think carefully before making any alterations, because the surrounding environment will also have an impact on what birds will use the nest box and whether it is in a suitable location or not.
You mention an old dead tree had been removed, but you don't mention what other trees or greenery you have in your garden and immediately surrounding gardens. That sort of info could help someone with workable suggestions.
You could include a photo without giving your exact location away, just to show what the immediate environment looks like.
Also, have a look at the following RSPB info: "Making and placing a bird box".
Finally, nesting will almost be finished for this year as adult birds will be more concerned with getting their latest broods and themselves ready for winter, and for some, that will include migration for our summer visitors. Apart from the weather and the fact the nights are now drawing in, there will be plenty of time between now and the end of the year to proactively locate the nest box with a view to birds becoming interested in it as a suitable nesting home next year.
https://www.rspb.org.uk/birds-and-wildlife/advice/how-you-can-help-birds/nestboxes/nestboxes-for-small-birds/making-and-placing-a-bird-box/
Mike
Flickr Peak Rambler