How would procurement manager handle conflict of interest if it arise?

Conflict of interest can occur in many different ways. The best way any procurement professional can manage this is to report the CoI to the major stakeholders to their purchasing project. If the CoI is well-understood, then a plan to mitigate can be developed. It really is case-by-case, but if it is something like a your procurement director having a stake in a company he would like to award a supply contract to, then it is important that you run a fair, balanced and comprehensive RFP process with the express exclusion of the Procurement Director, to ensure that the only way the contract is awarded is on the merit of their proposal when compared with other vendors.

Alternatively, you could simply exclude that supply from the RFP process, stating a recognised CoI as the reason.