I’ve come across the expression ‘to become irrelevant’ in Gossip Girl. Eleanor Waldorf (an aging fashion designer from Upper East Side) shared her fear that one day she would become ‘irrelevant’ meaning that clothes she designed would be regarded as uncool among youngsters, the target audience of her brand.

It means to stay important. That phrase is not used often. The term "relevant" is used more frequently however.. Again, it just means something or someone is important to an issue. Yusuke's advice was relevant to our decision. In that sentence it means important. However, it can also mean something relates. For instance. Yusukee's testimony was relevant to the case. In that situation it may not be important, or it may be, but it relates to the topic.