Question: Run Build and update Service sequence

[xpepermint]

I try to figure out the way of creating a common development sequence:

A: Update source code (manually) then run a single command that does:
B1: Build new image, then push it to DockerHub
B2: Apply changes by restarting Service with the new image (pull new image, start new revision)

Is this something that I can do with the Build file (just by defining all these steps or should I implement some advanced script or smth).