I’ll take the TOC and try to summarise contents of each chapter in one or two sentences.
Chapter 1 – Character Options
01.10: Lifepath Options
Contains six species wrtite-ups unique to this book.
01.20: Wartime Characters
Contains advice on wartime character traits, sample Values and Focuses and alternative Career Events to choose from for characters created in an environment of warfare.
01.30: Wartime Talents
Contains 14 Talents. I have not checked (yet) whether they’re unique to this book.
01:40: Wartime Roles
See above; 12 roles from Operations Division (6), Player’s Guide (4) and Command Division (1); 1 is unique to this book as far as I see. Descriptions are expanded.
Also contains advice on playing the Roles from the Core Rulebook in a warfare environment.
01:50: Weapons and Gear
Optional Rules on (shipboard) phasers and torpedoes. Not checked whether unique to this book, some rules felt familiar from Utopia Planitia. Yet, it might be that that book covered similar but not identical topics. I would have to refresh my memory on that. Includes rules for Planetary Defenses that I have not seen before in any STA supplement.
01:60: The Trauma of War
Introduces an alternative system of character development revolving around “scars” that builds on characters’ Values and their suppression in situations of war. Rules on casualties aboard the ship and PvP. Also, lots of advice on off-game safety in gritty settings and/or with PvP in the game.
Chapter 2 – Gamemastering the Campaign
02:10: Group Preparation
Advice on Session 0 and Player Safety. Refers to the checklist I have mentioned before that is super super helpful imho.
02:20: Planning the Campaign
Lots of background-information on the Federation-Klingon War and how to use it as a backdrop of a STA campaign.
02:30: Running the Campaign
Advice on different “types” of Missions a bit like the “Division”-supplements offered. Descriptions of “points of interest” that foreshadow the strategic overlay in Chapter 3. Contains advice on how to use and adapt the Mission Briefs in the Discovery Campaign Guide for the Strategic Campaign. Advice on pacing of the campaign.
02:40: Notable Star Systems
Star Systems for use as a backdrop of (an) adventure(s). Six in total with 2 in high detail and 4 in low detail. One detailed and two rough descriptions for each Starfleet and Klingon Empire.
02:50: Optional Rules
Advice on how to adapt the Strategic Campaign for an Admiralty Campaign instead of a Bridge Crew, or a crew of independent traders (or mercenaries), or a Klingon crew.
Variant rules on combat (introduction of “Reactions”), initiative variants. Also (each) a more detailed approach on power management (esp. during combat), chases and pursuit, and stealth and infiltration.
Chapter 3 – Campaign Rules
17 pages of an all-new strategic layer mini-game that simulates the allocation of resources during a war campaign. In essence, your players, in between missions, take the seats of admirals and/or their staff and decide which ships or persons within a fleet shall deal with several problems that pop up. They also decide upon which mission they want to deal with themselves with their main characters on the bridge of their ship. Outcome of each problems may influence each other; a failed roll on a problem on the strategic layer may complicate a mission as well as a successful mission may generate and/or improve new assets for the strategic layer.
If you’re interested in such a game, this chapter alone makes the book completely worth it! In my opinion, the rules blend in well with 2d20 and are able to provide a great and immersive benefit for the game while staying fast and unobstrusive.
Really, I love it already and can’t wait to try it out! 
Chapter 4 – Early War
Two full adventures, 8 mission briefs. Also, description of two scripted events (The Battle at the Binary Stars, Sarcophagus Destroyed) that can take place during Early War.
These missions are specifically tailored for the period of Federation-Klingon War. Yet, as always, they should be able to be tweaked to any timeline and faction with low-to-medium effort. I have yet to see the published adventure or brief that I’m unable to get some ideas from.
Chapter 5 – Mid War
Again, two full adventures, 8 mission briefs, two scripted events (U.S.S. Discovery Disappears, The Starbase Assaults).
Chapter 6 – Late War
Again, two full adventures, 8 mission briefs, two scripted events (U.S.S. Discovery Reappears, The Truce at Qo’nos).
Chapter 7 – Starships
07:10: Fleets of the War
Background information on how the Federation and Klingon fleets were structured during that era. Also optional rules on swarms of size 1 and 2 ships.
07:20: Federation Starships
Stats for 14 named Federation Starships of the Discovery era / Federation-Klingon War.
07:30: Klingon Starships
Stats for 15 named Klingon Starships of the Discovery era / Federation-Klingon War.
Chapter 8 – Allies and Adversaries
08:10: Federation and Starfleet
Stats for 9 NPCs.
08:20: Klingons
Stats for 5 NPCs.
Appendices
Three reference sheets for use in Session 0 (Safety Checklist) or the strategic layer of the campaign (Player/Gamemaster Campaign Tracker).
I hope that helps. 
My personal conclusion: Despite I’m not too much into DISCO as an era, the book was worth it. Some of the alternate/expanded/optional rules will prove valuable for all my games as a GM and the strategic layer – I simply love that one! 
For everyone into DISCO and/or a more sandbox-style game with lots of options for players where to go and explore next, in my opinion, buying this book should be a no-brainer.