"To conclude the case" means to bring the case to an end or to finish the case. It suggests that all the necessary actions have been taken and that there is no further need to continue or discuss the matter. Full definition
We handle brain injury cases on a contingency fee basis, there is no fee unless you successfully conclude your case. (justiceky.com)
I would like to take this opportunity to say «thank you» to you and your attorneys and staff for all of your hard work and determination toward concluding my case. (fleming-law.com)