You can use an existing command alias within another command alias. Define a first alias:
alias print lp
This creates the alias print for the lp command used to print files to your default printer.
This alias can now be used within another alias. For example:
alias tree 'cd; ls -R | print'
The alias tree will list the complete directory tree below the users home directory on the default printer. Multiple commands within an alias can be separated by a semicolon; just as they are on the command line.