The various checks that are required to get into Local Services Ads varies by business category. I put this together to try to help sort through it all.
All businesses must meet business license and owner license requirements specific to the state/province they’re in, if applicable.
Advanced Verification was originally required for moving companies but Google removed it in May 2019
Additional details can be found here: https://support.google.com/google-ads/answer/6226575
The table on that page was used to populate my data studio report above.