DBCC CheckDb on Secondary Asynchronous Replica
Can I run Ola Hallengren CheckDb job on a Secondary Asynchronous Replica (DR) that is readable during business hours?


Sure, assuming the routine doesn't try to update any command or history tables in that database (since it's read-only).


  ... and secondly if is safe as I have a primary server that is Live and I am doing a checkdb on a secondary during business hours/ off hours.


Much like sp_BlitzErik has stated, we can't tell you if it's "safe". This is going to depend on a host of factors such as disk space, redo queue size, send queue size on the primary, memory, current load, etc. Your best bet is to try it and see if you have no other metrics to go by - if people complain, you have your answer. If the website goes down, you have your answer. If no one says a word and everything goes well - you have your answer.