Repairing a detached cover on an old leather-bound, sewn book with marbled end papers
Definitely don't attempt to repair it yourself - I can't tell for sure from the photo, but I think this is a hollow back binding. In this style of binding the covers and the spine were build directly on the book block, not glued together separately and "hung" into the covers as is done with modern hardcovers. That makes fixing a (partially) detached cover harder.

In a modern hardcover, you would fix this approximately by:


detaching the end paper from the book block on the broken side,
lifting about an inch of the end paper from the coverboard,
pasting a strip of cloth or thicker japanese paper over the torn cover joint,
pasting a strip of thinner japanese paper over the torn end paper joint ,
reattaching the end paper to the cover board and the book block,
and optionally, painting the new material paper to match the surrounding if it's showing through.


Better hardbound books will have the book block attached to the covers not only by the end papers but also by paper,cloth, the ends of the tape/ropes the book block was bound on, etc. These can stay attached, since you can paste the patch over/around them.

In a hollow back... I'm not sure, to be honest. I never actually made one, although I know the approximate steps, and I definitely never tried to repair one. 

The main catch is that since the spine is constructed directly on the block, you can't just detach the end paper to get access to the joint. My best guess is that you would still detach the end paper from the book block; then you might need to cut a slit between the book block and the spine hollow to insert the patch. In best case scenario you would want to avoid opening the hollow, but rather insert the patch between the layers of the back "board" (it's not actually a board, it's several layers of paper pasted together).

If you plan to get this book repaired, definitely check the credentials of the professional. Check their portfolio if they have it, ask directly if they ever worked with this type of book. Hollow back binding is very common on older books, so you should find someone easily, but I assume it would be also easy to be a "professional bookbinder with book repair experience" without ever getting your hands on one. If you don't want to alienate the person, be the curious book owner and ask what kind of binding this is - the right kind of bookbinder will tell you a lot more than I could ;)

Also, if this is the only damage the book has and you don't use the book often... maybe the safest thing would be to leave it be. It doesn't look like a big tear. Store it in dark, dry place, avoid non-archival materials and pests, and it will be alright for a few more decades.