Next step(s) advice

Came back from abroad and felt the pile in my compost bin was feeling a bit too wet and was getting clumpy.
I've shoveled it out on what used to be our lawn (sun has killed it this summer so some nutrients can't harm it), assuming I can shovel it back in tomorrow once it's a bit drier and I've raked away some more at the clumps.

What are the next steps though with this? Let it age or mix in some more browns and keep chucking greens and kitchen scraps?

Thanks