Do you mean “all the active officers Companies House knows about (for all companies)” or “all the active officers for a given company”?
The first - you can make a request to get access to the officers bulk data downloads (search on this forum for how). That is their recommended way (and indeed the only way I think).
For the second, as far as I know there isn’t one - although the Companies Search web site allows you to tick to only see these.
People have been asking for this for a while.
You can change the ordering however. I believe currently the default order is that the “active” officers come first. This doesn’t save you from parsing the results to see if there’s a resigned_on field, but it does mean you may not need to request them all (Companies House have a “paged” API so if there are a lot of results you won’t get them all at once).
Details per here:
Good luck.