A couple off the top of my head:
* Trigger a reaction in a way that an ally could not use otherwise
* Modify Initiative rolls at the start of combat (for example, choose to subsitute the Warlord's History check then?)
* Grant out-of-turn movement (but neither action nor attack) at the rolling of Initiative
* Most Warlord granted-actions (I wager) would need to eat the receiving allies reaction up (much like how a battlemaster's extra attack does) as a balancing factor. This would prevent "stacking" actions (such as 3 warlord all using an extra attack power on a fighter in one round).
* My fear here is that Expertise would absolutely DESTROY using skills for Init. A 1 level dip for +4-+12 to Init? Sounds good. That said, granting an initiative bonus is an option.
* I'm thinking this could be handled with with "grant action: dash"
Now, the next thing to consider is what is the economy for using these powers. Right now, their are four major economies in 5e: Dice (superiority Dice, Bardic Inspiration Dice), Spell Slots (Spells), Per Rests (x amount per short/long rest) and Points (spell points and psionics).
Right now, let's rule out spell slots (we're not making a nomagical caster) so that leaves us with points, dice, or per rests. Per rests are good for auxiliary abilities (something you're not going to do every round or every combat, like action surge or rage), Dice seem unique to buffing or martial classes, which the warlord falls into, and points (at the moment) are just a more fine-tuned spell slot system.
The other thing to consider is what effect each should be granting. Bonuses come in a few types: bonus dice (bless, bardic inspiration), advantage/disadvantage, or static bonus (rare and usually unchanging) or unique effect (healing, removing conditions, granting an action).
Once we pick our power economy and types of effecs (Pay X to get Y effect) we will have to set prices and resources (how much x does y cost, how many x's do we get per day). At that point, its just a matter of playtesting to make sure things are broken.
Personally, if it were me, I'd be looking at a suped up Battlemaster as a base class (with more powers and many more dice) with some per-rest auxiliary powers and a few always on abilities (such the aforementioned bonus to init).
Good luck.