I understand this sentence
Vi chiedo di metterci impegno.
as
I ask you to dedicate some efforts here. (for instance a task has been given, I ask you to dedicate some effort to this particular task.)
Is this correct, or what nuance brings "ci" in metterci ? Is metterci impegno a fixed expression ? How would you translate or understand ?
This is not a fixed expression.
My understanding is that ci in this context is a demonstrative pronoun that stands for in ciò = "in this" (rather than an adverb, like "here").
Vi chiedo di metterci impegno.
is equivalent to
Vi chiedo di mettere impegno in questa cosa.
My literal translation would be "I ask you to put effort in this" but a more natural translation could simply be "Please, put in some effort".
