If you're deadlifting about as much as you weigh with a double overhand grip, there's no need to worry about your grip as a specific thing. The deadlift itself will develop your grip strength just fine for a while longer, with just a minor tweak or two.
The Least Intrusive Grip Improvements
The important thing to do is to challenge your grip as much as possible without interfering with your progress on the deadlift itself. For that, I recommend:
- A hook grip on your heaviest set
Chalk was a dramatic shift in my deadlifting. Not having the bar slip out of my hands from sweat was a game-changer with no discernable downside. I got a block at a rock-climbing store for a buck fifty and it's lasted me over a year with frequent use. Keep it in a bowl so you can capture the dust and fragments to use later.
I also recommend using an overhand grip for all warm-up sets, then switching to a hook grip for the work set (or sets). Since the overhand grip is weak, you will be requiring and and creating grip strength on all your warm-up sets (particularly the last). Using the hook grip when it's really heavy gives you a major grip strength boost. This will prevent your grip from getting in the way of big weights, or distracting you from proper form.
This double-overhand/hook-grip combination should prevent your grip from hampering your deadlift until you are lifting approximately double what you are now, or more.
I'd recommend against straps or grip-specific work unless they become absolutely necessary, and even then I philosophically prefer exercises that have other benefits over grip-strength-specific work. For instance, pull-ups, particularly on a rope, fat bar, or other hard-to-grip setup are great for your grip and also improve a whole lot of other strengths. Farmer's walks are another great, fun, productive way to work your grip while also improving posture, conditioning, and muscles across the trunk and legs. I'd do these before resorting to grippers.