I've a customer that brought me on as primarily a systems and compliance consultant and my responsibilities look to expand into helping manage and update their Terraform managed infrastructure. I've not yet used Terraform and will need to get up to speed on it. Should I bill all of my time learning it or eat some of the cost? If it was something they designed in-house I would bill all of it as the skills don't directly translate to skills for other customers but this makes it a bit of a grey area.
As freelancer I've billed hours for literally reading a book at home. They wanted me to know and be able to debug a critical storage system if something goes wrong. I believe my fees were still lower than finding another person.