There are many ways. The "best" option depends on the design of your user interface and sometimes it just comes down to your personal preferences.
The easiest to implement is to set up a portal to the Application Table on a layout based on Utility Allowance. If you enable "Allow Creation of records via this relationship" for Application in the relaitonship linking these two tables, You can add a new record in the portal simply by entering data in the bottom blank row of the portal and the primary key from Utility allowance will be entered automatically.
On a layout based on the Application Table, you can format UAAllowance as a drop down list/pop up menu of values from __PKUtitltyAllowance. This value list can include a second field from the Utitlity Allowance table in a secondary column to help the user select the correct value in the list.
There are ways with script triggers and either a global variable or global field to "synch" the current record on a Utility Allowance table with a layout for the application table and then you can set an auto-enter calculation that copies this value from the global variable or field.
Other options are also possible.
I went with the Global Variable. Thanks Phil .