Suu Kyi is the daughter of the country's martyred independence leader, Gen. Aung San. Her National League for Democracy party is the country's largest legal opposition group, and it retains the loyalty of millions of citizens despite two decades of repression.

Does the definite article imply Suu Kyi is an only daughter?

I don't think you can make that assumption.
Using "the" here emphasizes the tie between daughter and father. Using "a daughter" would water this down, so to speak. Using "the" does not at all rule out the possibility of other daughters, but focuses the sentence on this particular daughter.
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I thought I included the link. Anyway, here it is.

GG, If she had sisters, wouldn't 'a' be more appropriate? Can I replace it with 'a'?

 Delmobile's reply was promoted to an answer.
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Thanks, Delmobile.
Nice response Del. Way better than mine.