Short answer
Herbert's 55 check is the first step of the main quest Security Checkpoint: Democracy, which opens after Election Fever. At 55 reputation you can talk to him about election security, but convincing him needs 60 — and that first talk does not give you the missing 5. Finish another Herbert quest in between, then return to the Barracks.

Battle in the Town
View full-size image ↗Official promotional screenshot · © Lazy Bear Games / tinyBuild · Official media kit · Material credits
Who Herbert is
Herbert is the head of the guards at the Barracks in The Town. He has the Keeper bury the fallen and sends you into the battles against the zombies.
He is tied to 15 quests, from Certificate, Please at the start to Still Standing on Stilts.
The 55 and 60 checks
Security Checkpoint: Democracy has two steps. Step 1: speak with Herbert at the Barracks about security during the elections — needs 55+ reputation.
Step 2: convince him to handle security — needs 60+.
Finishing it unlocks Campaign of Thrones, together with Vote Early, Vote Naughty and Destiny Polls.
Where his reputation comes from
Certificate, Please (bring him a Burial Certificate) and Grave Expectations (raise graveyard quality to 10) are early +10s.
Herbert and? asks you to hand him a Love Novel at the Barracks, and The Nun Also Reads has Agatha read to him.
Not in Shining Armor Yet asks for 5 Steel Armor — each is 4 Steel Ingots, 4 Steel Details and 4 Fabric, so stock steel from the Bishop first.
Reporting victories in his battles also raises it. At 20 reputation the Reinforced Plank technology becomes available.

The graveyard from the official media kit. Raising its quality to 10 is one of Herbert's early requests.
View full-size image ↗Official promotional screenshot · © Lazy Bear Games / tinyBuild · Official media kit · Material credits
His full quest list
Certificate, Please; Grave Expectations; Swords and Bell; Fighting Spirit Required; First... Sludge?; Sad Captain, No Action; Herbert and?; Safe zone.
Security Checkpoint: Democracy; Reader for a Warrior; Not in Shining Armor Yet; Water Locked; Steamy Royal; Dirt Rights; Still Standing on Stilts.
Why it matters for the ending
Herbert is one of six characters who each ask for 90 reputation before the final battle — 100 if you keep the Red Eye. See our endings guide.
Sources
Related pages
Official artwork · © Lazy Bear Games / tinyBuildGuidesGraveyard Keeper 2 Endings
Official screenshot · © Lazy Bear Games / tinyBuildThe TownGraveyard Keeper 2 Undead Army
Official screenshot · © Lazy Bear Games / tinyBuildGuidesGraveyard Keeper 2 Graveyard Layout
Official screenshot · © Lazy Bear Games / tinyBuildEconomyGraveyard Keeper 2 Steel Ingots and the Steel Anvil
Official screenshot · © Lazy Bear Games / tinyBuildProgressionGraveyard Keeper 2 Church Organ
Official screenshot · © Lazy Bear Games / tinyBuildThe TownGraveyard Keeper 2 Battles