I want to use an accessorydisclosureindicator to inform the user to tap on the cell in order to change the time.
I did set the accessoryType to UITableViewCellAccessoryDisclosureIndicator in the cellForRowAtIndexPath delegate method but the disclosure indicator is not visible as you can see on the screenshot below.
How can I fix this?

I'm guessing that you already found this but I think that you want the editingAccessoryType.
http://developer.apple.com/library/ios/documentation/uikit/reference/UITableViewCell_Class/Reference/Reference.html#//apple_ref/doc/uid/TP40006938-CH3-SW61