For our customer the application which is running is using MySQL database. However, this server is without monitoring. I want to install OpenNMS (which uses PostgreSQL) application to monitor the solution and send the traps to main NMS system.
Is there any problem having both on the same server?
No, there is no technical problem. Both default to different ports they listen on.
The only problem that could arise is that each individual DB might be slower compared to an installation on separate phyiscal machines because they are both share (and fight for) for the same resources (I/O, memory, CPU, network, ...)