In reply to GrahamD:
The Rails Road car park does get busy but I think I've only ever been there once and not found a space.
When it is busy most of the people parking there are local dog walkers who don't tend to stay long, so you might find you only have to drive up the hill to the end of Woodbank Rd to drop your pal with the gear, turn around and come back down to find a spot. (The public footpath that gently descends down below the crag from there is sometimes soggy but a nicer walk than the pavement alongside the A57.)
I think there will continue to be issues once the Yorkshire Water car park does re-open. Pre-pandemic it was open from 8am - 8pm in the summer, but they just closed the gate and looped the chain over the stone gatepost without actually locking it if there was anyone still there. When they finally re-opened it after the pandemic, the gate had been replaced and they'd begun to lock it for real at 6pm. Hopefully when that car park it re-opens again they'll be a bit more pragmatic, or it's going to be a bit useless anyway.