The phrase "actua bajo la modalidad de contratación" is a bit confusing as to determining the context of the phrase in question, but using the translation philgoddard gave below "has obtained", I would conclude that the best translation for the phrase would be "has obtained a Civil Responsibility insurance policy covering...". I've seen the phrase "seguro a través de poliza de seguro" before, and although convoluted, I've sometimes simplified it to "insurance policy" depending on the context of the sentence. Although if anyone else has seen that (odd) phrase before and has a different solution I'd be interested in hearing what they've done with it.
(Note: I've seen "seguro a través de..." to specify where someone gets their insurance: employer, broker, university, etc., so depending on the specific context, another possible solution is to say that the phrase is used to specify that someone has a direct contract with an insurance company, as opposed to one obtained through a third party- although that doesn't seem to make sense in this context.)