For every apocalyptic battle in the Horus Heresy, there's another small-scale action taking place in secret - whether fought by elite strike forces, bands of insurgents, or decimated survivors trapped behind enemy lines. If you want a way to play skirmish style games and even campaigns focused on these small but pivotal battles, you could do worse than the Strike Team rules for Warhammer: The Horus Heresy, a fan project by the Toronto-based Heresy player Hazel.
There have been other takes on this idea: Extermination, the third of the Forge World Horus Heresy books, included the 'Tactical Strike' rules for first edition Horus Heresy, designed for skirmish games between extremely battered and isolated Astartes formations. And there are great fan projects making Heresy era unit rosters for Warhammer 40k: Kill Team. Strike Team caught my notice because it's an expansion to the current edition of Horus Heresy, and it's a very cleanly written set of fan rules.
You can download it from Google Drive here. According to Hazel's introduction, "The game initially started as a Trench Crusade total conversion and still borrows from that system (especially in regards to some of the earlier missions, and campaign progression which people seem to like), but now mostly uses the main Heresy 3.0 ruleset with some poached mechanics from Necromunda".

The biggest rules changes from third edition Heresy is replacing the I-go-you-go turn sequence with alternating activations, and tidying up the loose ends this creates around reactions and the morale phase. The rest comes from the general expectations of how you'll play - it's geared for campaign play, and campaigns themed around pretty desperate battles.
The game uses the regular Heresy force organisation system, but each slot provides a single model, not a whole unit. The command echelon is restructured: regular High Command units are not available, with Command units filling their space, while squad Sergeants get promoted into the normal Command slot.
As with the popular Centurion mod, extra limits are in place to cap the power of units in play: there's a points premium for models with Toughness five or higher, a hard limit of taking just one model with four or more wounds, and each force can only bring a single transport vehicle.
One key concept borrowed from Trench Crusade campaigns is glory points, which are earned by completing 'glorious deeds' in missions. This is a parallel currency that limits the weapons and equipment available to warbands to keep things fairly grim and gritty: Artificer Armor, Terminator Armor, and high powered weapons cost Glory Points instead of regular points.

There are other classic campaign system goodies. The tables for injuries and skills aren't too dissimilar to what you'd see in Necromunda, and there's a work-in-progress exploration system based around exploring a Hive city that has big Mordheim energy. Then there's the warband-wide "Ammo check" threshold, similar to a system from the first edition Tactical Strike rules: your marines' guns risk running dry mid-mission, but exploration events may allow you to stock up and increase the odds of passing Ammo tests.
I haven't tested it yet - I just think it's neat. If you're based in Toronto and want to join a really active Heresy scene, or want to give Hazel feedback on the rules, you can reach them in the Hogtown 40k Discord server.
If you're a Heresy player with an army to share, or you've come across some fantastic homebrew rules, we'd love to hear from you in the Wargamer Discord community!