You should read the agreement (contract) between your Owners Corporation and the strata manager. Find out the start and end dates of your agreement and the rules for terminating an agreement. If you hold a general meeting just before the agreement is due to end, there would be a motion to renew the agreement. If a majority votes against that motion, the agreement can’t be renewed.
If you wish to terminate the agreement and appoint a new strata manager at the same meeting, I think you would have to submit the agreement for the new strata manager when the agenda is distributed. People need to see the agreement before they vote to accept it. Are you happy for the old strata manager to see your new contract?
In my strata plan, we held an EGM requesting the strata manager change some parts of their agreement. They said that if we voted in favour of these changes, they would resign from our service. We voted in favour. They resigned.