裏切り者の素性を追ってみれば、その裏切り者が家族の厄介者だとわかるでしょう。

、。

If you trace the traitor's background, you'll find they're the black sheep of the family.

Literal

Traitor [possessive-の] identity [object-を] follow-try [conditional-ば], that traitor [subject-が] family [possessive-の] troublemaker [quotative-だと] will-understand [conjecture-でしょう].

素性を追ってみれば (if you try tracing their background) uses 素性 (background/identity) + 追う (to trace/follow). 家族の厄介者 (family troublemaker/black sheep) uses 厄介者 (nuisance/burden). A complex conditional sentence with narrative flair.