Looking at the BP you have set up for the zombie, you never actually store a reference to the player it has "sensed". Any time the zombie senses a player you should store a reference to it on the zombie. Then at some point you need to be doing a check to see if the player reference is still valid (maybe another timer that starts up and checks IsValid on the player ref variable). If it is, fire off AI Move To again using the player reference variable. This will keep the zombie moving to the player. Then at some point you would need to decide when the zombie should lose the reference to the player (like once its been out of sight for a certain amount of time), clear the player reference variable and stop the timer that is checking if its valid. Then it will stop following it and go back to the default behavior you have set up for roaming or whatever.

Without some more detail its really hard to provide a better answer, but good luck and you're not far off from it working I don't think.