Her unquestioned probity helped win her the respect of her fellow judges.
Her here acts as the Indirect Object: the beneficiary of the winning achieved (presumably) by this jurist's many excellent personal qualities.
This is not an uncommon or literary use, although it is more usual to express the beneficiary with a preposition phrase:
Olmos' field goal with just 30 seconds remaining won the game for the Tigers.
Her unquestioned probity helped win the respect of her fellow judges for Judge Harwell.
But note that in this particular case putting the for phrase at the end creates an ambiguity: was respect won for her or was it respect for her that was won? And with the pronoun, for her, the phrase is really too 'light' (has too many words) to follow the much heavier direct object the respect of her fellow judges. Bare her in the ordinary Indirect Object location is really the best choice here.