かけ in this case is just the verb stem. (Some textbooks also call it the ます-stem, because you can derive it by removing ます from the regular polite form of a verb.) It is used in many different ways, but here as you can already guess by the translation it just connects the sentence parts.
As was mentioned it connects the parts, which in spoken Japanese is usually done by using the て form, which you probably know. This is just a way of doing that that is only used in written Japanese.
But as a general word of caution, take any sentences taken from Tatoeba with a grain of salt. They haven't necessarily been written by, or checked by, native speakers.
Use of 掛ける (かけ) to apply brakes
As far as I can tell, かけ is the verb 掛ける, "to apply, or put on" in this sentence. But I'm not familiar with the かけ form. Lil' help?