"My father is working at a company."
The て form has many uses. Among other things, it's used as an imperative, and it's used to link two activities together, regardless of tense. When it's combined with 〜いる, as it is here, it forms the present progressive (~ing in English). つとめています means "is working," which is how Japanese people describe their jobs. In English, we'd simply say "works."
Japanese sentence structure goes Subject - Object - Verb. If you want かいしゃ to be the object of the verb つとめています, it has to come after 父, otherwise you're just telling us where the action is taking place. So instead of saying "My father works for the office (lit. is serving the office)," you're saying "At the office, my father is working (lit. serving)"