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Those who don't know how to be silent are not skilled speakers.
Literal
Be-silent [thing-こと] [object-を] not-know person [topic-は] talk-skilled [topic-cop-では] is-not.
Aphoristic claim built around two nominalizations and a relative clause: 黙ること ('the act of being silent') is the object of 知らない ('not know'), and the whole phrase 黙ることを知らない modifies 者 ('person, the one who…'). 話し上手 is a compound noun (話し 'talking' + 上手 'skilled at') often translated as 'a good talker.' ではない is the negative copula in plain form.