The best replacement for possessive pronoun is possessive adjective.

The best alternatives to possessive pronoun are rated as following:
★★★★★  possessive adjective
★★★  adjective
★  contraction
  determiner

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Speaking about possessive pronoun, one probably shouldn't forget about gerund.

Other search terms related to possessive pronoun and their ratings are:
★★★★★ gerund
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possessive pronoun
possessive adjective
adjective