You just need to bind a variable to the [tabIcon] property and then update the value of that variable:
In your template:
<ion-tabs [selectedIndex]="tabIndex" name="event">
<ion-tab [root]="tab1Root" tabTitle="Discover" [tabIcon]="discover.icon"></ion-tab>
<ion-tab [root]="tab2Root" tabTitle="Search" [tabIcon]="search.icon"></ion-tab>
<ion-tab [root]="tab3Root" tabTitle="Me" [tabIcon]="me.icon"></ion-tab>
<ion-tab [root]="tab4Root" tabTitle="My Events" [tabIcon]="myEvents.icon"></ion-tab>
</ion-tabs>
In your component:
this.discover.icon = 'beer';