It's easier to find books on the monarchy in general; not many have been written yet about Elspeth specifically.
Valdemar, compared to most, seems to be a remarkably stable country. While there has sometimes been politics around the succession, even rising to the level of drama, there has never once been a true crisis. The Companions have a lot of sway in Valdemar; if they're backing a particular candidate, that goes a long way. Also, pretty much anyone with Gifts ends up as a Herald, unless they're a Healer or Bard, and the Heralds are - well, more like a family than an organization or guild, in a lot of ways. Whether or not they're actually impossible to corrupt, as is claimed, they stand together. Plots within the Council, even the occasional coup attempt, have been known to happen, but division within the Heraldic Circle is unheard of.
Elspeth's reign does seem to have been unusually peaceful and prosperous, though some of that might be attributed to luck. She is claimed to have put more time and effort into diplomacy than most rulers; early in her reign, she made multiple trips per year to visit neighbouring countries and schmooze with their leadership. She's said to be charismatic. The Council almost never votes against what she wants.
It's mentioned that the alliance she brokered with Iftel, Valdemar's neighbour to the northeast, involved a state marriage, but the book doesn't even give her husband's name, just mentions that he died about ten years ago.
The overall theme of Elspeth's policies is 'boring'. She reformed some tariffs on trade across the border. Inasmuch as Valdemar has any monetary or economic policy to speak of, she seems on top of that. She took the existing census-process, which used to be run ad hoc whenever a particular ruler felt like it, and made it a standardized process once per decade, then set up a system where the data collected could be used to revise the Heraldic circuits and track placements of Healers.