I'm gonna be perfectly honest, 1E never really had a solidly mobility-based class or archetype like what existed in 3.5.
What few options existed (Scout Rogue, Mobile Fighter, Monks' Flying Kick style strike) were put in place to make mobile warriors not suck from a DPR perspective compared to those focused on full-attack-actions.
Given the 3 action system and 2E's overall increased allowance of mobility by restricting AoOs to opt-in, we could more easily have mobility focused archetypes and builds now.
Maybe some mounted combat and vehicle rules that aren't convoluted and can be easily used! That would be nice for mobility.
Love me some more classes.
First buy/rent/steal these classes from their respective owners.
All of Dreamscarred Press's Psionic Classes
Rite Publishing's Luckbringer
TPK Publishing's Malefactor
A World of Warcraft style Death Knight/Anti-paladin
Then stat me up some of these classes:
A no-spells Ranger
A Shaman class that lets me play Fool Wolf
An Apothecary -- non-spellcasting mundane healer/buffer
A Medieval-punk Engineer
Eldritch Knight and Arcane Trickster style core classes
A courtier/diplomat class that was better at the fast talk than the head bashing
Although the OP is leg pulling a bit, a wheelman/zoomer logistics/quartermaster class might be interesting. Give it some fixer connections like The Wolf in Pulp Fiction, a bunch of merchant/scrounging abilities like Crapgame in Kelly's Heroes and a solid skill background in the explorer leg of <insert your favorite adventuring game here> and it would be playable at a table that wasn't purely Murderhobo.