Changing part of filename

I just want to change part of filename, in my case the number, from 000 to 001 and so on. I have so many files so it would be easier to do it in groups of about 20 files. Is that a way? The rest of the filename need to be untouched.

I don't quite understand - you want to increase a number by "1"?
Or do you simply want to replace an existing number by a different one?
Best for better suggestions would be a real example.

And please let us know where you get the new number from?

An example with your current real filename and your new filename would help a lot.
A screenshot from your fields in Alt+ T where you probably get your number would help too.

The number is my way of organize a lot of music files into a larger work. I found out after about 35 pieces of music that I wanted to place some files before the ones that were already named.

I want to replace the number in the start of the filename, only the number.

As I said: a real example would help a lot.
Without that:
Try Convert>Tag-Tag for _FILENAME
Format string: $num(%_counter%,3) - $regexp(%_filename%,\d+ ,)

Thank you.
So select all files as %_counter% always starts at "1".
Then use the following
Format string: $num(%_counter%,3) - $regexp(%_filename%,\d+ - ,)

All this files I want 001 in the start, and the following will therefore also need a change.

Please show us some NEW file names as you would like them after renaming.

001 - From the Earth to the Sky 01 - Medieval sacred ballad

Please show us 3 examples to see the principle behind it.

Like
OLD:

000 - From the Earth to the Sky 01 - Medieval sacred ballad
000 - From the Earth to the Sky 02 - Medieval sacred ballad
000 - From the Earth to the Sky 03 - Medieval sacred ballad

NEW:

001 - From the Earth to the Sky 01 - Medieval sacred ballad
002 - From the Earth to the Sky 02 - Medieval sacred ballad
003 - From the Earth to the Sky 03 - Medieval sacred ballad

or
NEW

001 - From the Earth to the Sky 01 - Medieval sacred ballad
001 - From the Earth to the Sky 02 - Medieval sacred ballad
001 - From the Earth to the Sky 03 - Medieval sacred ballad

The last example is the right, because they have all the same title.

So you just want to replace all occurings of 000 with 001?

So all the files in the picture should have 001.

Yes, more than 30 pieces of music in many musical variations.

Then use
Format string: $replace(%_filename%,000,001)

I do not have much hope to define a criterion that increases the generated number unless you use the track numbering wizard Ctrl-K with a suitable criterion like "New disc on change of TITLE" and you write that number to DISCNUMBER.
Finally, you create a new filename from tags with that DISCNUMBER at the front.
Otherwise I see no way to automate that.

It's importante to keep the rest of the name.

I do not need to increase the numbers in the group.

That makes it more difficult.
Have you tried the track numbering wizard and checked what it wrote into DISCNUMBER?