syntactic analysis - Unclear grammar of present continuous — is it present continuous?

A clerk taking cash from a customer and not entering it in the cash register.

Here's my question: how and when can I use subject + verb + ing without be like the first part in the sentence?

For me, I'll say: "a clerk takes cash" (present simple) or "a clerk is taking cash" (present continuous). Sometimes, I see sentences like the one mentioned above, but I can't detect what kind of tense that is. Under what conditions should I use this subject +verb + ing form?