Grassroots Club is a community CrossFit gym at 4 Hands Rd in Middleton, Christchurch, rated 5.0 on Google from 61 reviews. Its website describes conditioning, weightlifting and gymnastics sessions scaled for every level, with an ice bath and saunas for recovery, and a one-month minimum membership.
CrossFit style training is built around coached group sessions, so ask how the coach scales each workout for your level before you start. Olympic lifts need careful technique, and a good coach will spend time on form before adding weight. Check the cancellation and pause terms before you join, since gyms vary a lot on how they handle these.
For Christchurch locals who want coached group sessions in lifting and conditioning, Grassroots Club on Hands Rd is worth a look.