1
general::
Phrase(s): with a will
with determination and enthusiasm. • The children worked with a will to finish the project on time. • The workers set about manufacturing the new products with a will.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Vigorously, energetically, as in He started pruning with a will. This term, first recorded in 1848, uses will in the sense of "determination."
American Heritage Idioms