。
She has close ties to the company.
Literal
She [topic-は] that company [with-と] close relationship [subject-が] exists.
~と関係がある ('to have a relationship/connection with X') uses と to mark the other party in a relationship — を would be wrong here, since the relationship is mutual rather than directed. 密接 ('close, intimate, tight') is a formal adjective for relationships, ties, or connections; you wouldn't use it for emotional closeness (親密 or 仲がいい would fit there). The double-subject feel of [彼女は] [...関係が] is the canonical Japanese 'X has Y' pattern: は marks the topic, が marks what exists, and 'has' emerges from context.