I would say that Theros (mythic play) is a counterpoint to that.
That is an expansion of the base rules in the PHB and it is optional. The issue, as I see it, is that gritty play involves a restriction on the options in the PHB.
To get gritty play as I see it, one would have to:
1) No ASI on level up. This makes lower level monsters more relevant for longer. I would allow feats though.
2) No long rests in the wilderness. Long rest needs a secure base in a town village or fortified camp guarded by hirelings.
This would be the minimum and I could see some as regarding it as not gritty enough.
For extra grit:
Characters start off as sidekicks and get promoted in to classed characters. Add in a lingering wounds system, like every time a character fails a death save they pick up a lingering wound.
For lack of low level magic, make the full casters multiclass to at least 3 levels in another class.
None of this, is stuff that I could see WoTC as ever officially supporting. If you have a different view of what is gritty play I am interested in hearing about it.
Of course for a real old skool feel make 'em roll 3d6 in order

. I, of was a generous DM back in the day. I allowed roll 3d6, 7 times, pick the best 6 and if the ability mods added up to less than 2, I allowed a reroll.