Define alias that references other aliases

Following @anubhava's sage advice:

foo() { echo foo; }
bar() { echo bar; }
foobar() { echo "$(foo)$(bar)"; }
fooandbar() { echo "$(foo)and$(bar)"; }

Spaces and semicolons inside {} are required there.

To reuse alias in another alias use:

foobar='foo;bar'

However I would suggest you to consider using shell function to get better control over this.