I remember reading a review of this book around 2000, though I do not know when it was actually written. I believe that the soldier was killed during an investigation of some sort. His clone is sent as a replacement to find out what transpired.
It could be Duncan Idaho in the Dune series (Dune Messiah and/or God Emperor of Dune). Frankly I can't recall the specifics, but I seem to recall that in at least one of them, the new Idaho clones had to undergo a certain trauma or imprinting in order to regain their past-life memories.
This played a role in several of the books including Heretics of Dune and Chapterhouse: Dune. IIRC, there was also a ghola of a commander Teg.
The clones were called "gholas."
It reminds me of #2 in Mike Resnick's The Widowmaker series - Widowmaker Reborn:
also Walter Jon Williams' "Voice of the Whirlwind" might fit even better
This sounds a lot like Today We Choose Faces by Roger Zelazny. Protagonist is an assassin who uses cloning and memory transplants in an attempt to guide humanity. The final clone ends up having to pull up the memories of the the very first instance, Angelo di Negri.