No, as Irish citizens’ rights to continue residing in the UK are protected under the UK-Ireland Common Travel Area arrangements.
Hence, Irish citizens are not required to apply under the EU Settlement Scheme. However, if you need to sponsor a family member for settled status, obtaining settled status for yourself beforehand would make the application process easier.
Nonetheless, it bears emphasis that this refers specifically to the application process for sponsoring a family member for settled status rather than obtaining it for them. If they are an EU citizen, they will need to make their own application for settled status under the EUSS. For more information on this, please call 0208 215 0053.