The officially released 2-disc soundtrack for the original anime adaption actually lacked a LOT of the music which was used, it'd have been enough for a third disc easily, but it wasn't done for whatever reason. Perhaps some of it was legal reasons, as there was some licensed stock music used for a few bits or mixed into tracks, but it wasn't a lot, and typically that kind of stuff is actually covered in said licensing.
Someone contacted Yasushi Ishii about it not that long ago and asked about whatever happened to that music, and he was actually cool enough to plain hand some of it over. This leaves a few things, particularly variants of some songs (instrumental variants for instance), some which just wasn't saved apparently, but this still plugs a lot of the 20+ year gaps.
https://youtu.be/wNPoM3Bi7yEhttps://youtu.be/YesdOaq0zrwhttps://youtu.be/nQeQkRv0KC8https://youtu.be/cONKOpUAD4Qhttps://youtu.be/3U-V6kgpP2ghttps://youtu.be/hrYZtdoXImkhttps://youtu.be/32w0swPHLzkhttps://youtu.be/vEqRB8VcZAMhttps://youtu.be/xb-DJqEtcYMhttps://youtu.be/sn7nmnLwWN4There's yet more than what I linked, just search YouTube for "Hellsing Soundtrack Unreleased"
The last one I linked in particular is one which gets me a lot, because it's one of the most memorable tracks in the series, but none of the released or leaked versions of it are quite right. This one has added vocals, is mixed differently, and the pitch/tone of the piano is noticeably a lot higher, along with some skips.
Apparently this is one of those where a lot of the WIP and alternate stuff was lost, so there's just these pieced together versions from older leaks, the new stuff Ishii released, and I think imitations.