"Second nomination" refers to a subsequent or additional proposal or suggestion made for someone or something to be considered for a specific role or recognition after an initial nomination has already been made. Full definition
Joe Ganim seconds his nomination for governor during the Democrat convention. (courant.com)
Role opposite Mark Wahlberg in boxing movie The Fighter brings Melissa Leo Oscar success on second nomination (theguardian.com)
Ang Lee's second nomination as best director underscores the diversity of his films; he was named in 2001 for «Crouching Tiger, Hidden Dragon.» (rogerebert.com)