The Expense Create and Edit screens are custom SalesTrip lightning components. In order to add additional fields to these screens, you need to follow a few steps
Create the field on the SalesTrip Expense object as you would for any other Salesforce Object. This is done through the Setup Menu -> Object Manager -> Expense (salestrip__Expense__c) -> Fields & Relationships. There is lots of content available from Salesforce on how to do this:
Salesforce Help & Training: Custom Fields
Trailhead: Customize a Salesforce Object
Ensure you do not create any required fields without a default value, as this will break SalesTrip Expense creation functionality in a number of areas.
Create Field Set
For each type (or types) of Expenses you wish to use these fields with, create a Field Set on the Expense object, and add the field(s) you wish to show on the Expense create / edit screen for that type (those types). This is done through the Setup Menu -> Object Manager -> Expense (salestrip__Expense__c) -> Field Sets.
Give the Field Set a Label, Name and Description, then drag and drop to add the fields to the field set, and save.
Update Expense Type Configuration
SalesTrip needs to be configured to use the Field Set you have created with the appropriate Expense type(s). Navigate to Setup -> Custom Metadata Types -> Click "Manage Records" next to "Expense Types".
This screen will show a list of your Expense Types, but if you modify any Expense Types in the global value set you'll need to also update them here.
Either find the existing record for the Expense Type you want to configure (you're looking for the value in the API Name field on the global value set, in the Label field of the Metadata record), or create a new one.
Put the name of the Field Set in the “Additional Fields” field and save.