Since "fee" generally connotes compensation for a professional service rendered, this word is a bit too narrow a translation if "Engelt" is used more broadly in the given context. If professional services are involved, then it is probably the better translation, however.
There are multiple definitions - click on the translation that matches your context.
the amount of money paid for work carried out by a professional person, such as a lawyer or an accountant
The boss of the NHS's legal unit says escalating costs from no win, no fee solicitors are draining resources from patient care.