An emergent bilingual learner is a learner who is in the process of becoming bilingual. Garcia et al. (2008) use this term to refer to children who speak a language other than the language of schooling at home and learn to function in a second language at school. 

García, Ofelia; Kleifgen, Jo Anne; Falchi, Lorraine (2008). From English Language Learners to Emergent Bilinguals. Equity Maters, research review N°1, Campaign for Educational Equity.