If the Head of House has promoted you to become the new Leader, you will receive an inbox message regarding the promotion.

A blue box will then appear on your 'About' tab on your Fashion House page. Tap on the “” to accept the promotion. This blue box will remain on the 'About' tab until you accept the promotion, or unless the Head of House cancels the promotion.

 
Once you accept, you will be the new Head of House!