。
She ignored my advice and kept seeing him.
Literal
She [topic-は] my advice [object-を] ignored [and-て] him [with-との] association [object-を] continued.
Two clauses chained by the te-form 無視して ('ignored, and...'). 交際 ('association, social relations, dating') is a Sino-Japanese compound that often carries the romantic-relationship sense, especially when paired with a person — 彼との交際 ('dating him,' 'her relationship with him'). The compound particle との is a fused との where と marks the partner and の turns the result into an attributive ('the [association] with him'). Continuing or breaking off 交際 is the standard Japanese vocabulary for a dating relationship.