Change icon when click button ionic 2

You could use *ngIf directive here to show conditional icon.

<button clear text-center (click)="toggle()">
   <ion-icon name="arrow-drop down-circle" *ngIf="!visible"></ion-icon>
   <ion-icon name="arrow-drop up-circle" *ngIf="visible"></ion-icon>
</button>

You could use name property instead of creating two different ion-icon

<button clear text-center (click)="toggle()">
   <ion-icon 
       [name]="visible ? 'arrow-drop up-circle' :'arrow-drop down-circle'">
   </ion-icon>
</button>

You can create a conditional in the name= attribute

<ion-icon [name]="visible ? 'arrow-dropdown' : 'arrow-dropup'"></ion-icon>