"立为嫡嗣" can be translated into English as "to be designated as the legitimate heir" or "to be established as the primary successor".
Here, "立" means "to designate" or "to establish," "嫡嗣" refers to the "legitimate heir" or "primary successor" in a traditional Chinese context, often the eldest son or a son born to the primary wife in a patriarchal lineage system.
Both translations capture the essence of the original Chinese phrase, emphasizing the formal designation or establishment of someone as the rightful successor in a line of succession.