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The company president is the kind of person who gets it.
Literal
Company-president [topic-は] talk [attributive-の] understand [attributive] type [attributive-の] person is-[copula-だ].
話の分かる is a stock phrase for 'one who gets it, who understands (the situation, reasonable discussion).' Uses 話 ('talk, discussion') + の attributive substituting for が + 分かる — the が→の substitution in a relative/noun-modifying clause. タイプ is a loanword noun 'type, kind.' A compliment implying the president is reasonable and approachable, not an unbending authoritarian.