"Sing and play" is a way to describe playing a musical instrument while singing at the same time. "Play and sing" is also a common way to describe this activity. Here are a few examples:

She's really talented at singing and playing the guitar at the same time.
He's a one-man band - he can play and sing just about any song you can think of.
Have you ever tried singing and playing the piano at the same time? It's not as easy as it looks!