The phrase "to conduct an inquiry" means to investigate or examine a particular topic or issue in a thorough and organized manner to gather information and find answers or solutions. Full definition
Earlier this year my 12th graders conducted an inquiry into education. (mrjblock.com)
(b) any document created by a person conducting an inquiry or arbitration, for the purposes of the inquiry or arbitration. (publiclawforeveryone.com)
Most financial institutions conduct an inquiry when you open a new account, so opening an account at a big bank or a small credit union have similar consequences for your score. (nationalcreditfederation.com)