"立为嫡嗣" can be translated as "to be designated as the legitimate heir" or "to be established as the primary successor" in English.
Here, “立” is translated as “to be designated” or “to be established”, indicating the act of formally appointing or recognizing someone. “嫡嗣” refers to the legitimate or primary heir in a family line, often the firstborn son or the son with the highest status in terms of inheritance rights. Therefore, the translation captures the essence of being formally recognized as the primary or legitimate successor in a family or lineage.