THis is not possible in FileMaker. You only get a fixed number of tab panels created in layout mode when the tab control was added to the layout. The only way to add another tab panel is to return to layout mode and manually add another tab.
You'll need to use an alternative layout/data design to achieve the same result.
Do you have any suggestions as to how I can get around this problem?
You won't be able to add new tabs on the fly.
Just from looking at your screen shot, it looks like you want to document an "incident" between two or more individuals and that you want to add a tab for each individual involved.
If this is the case, I'd take a look at using a portal where you link in/add as many inidviduals as you need to document the incident. This could be a many to many relationship issue where a given individual can be involved in more than one incident and an incident can list more than one individual.
If that's the case, start with these relationships:
Incidents::__pkIncidentID = Individual_Incident::_fkIncidentID
Individuals::__pkIndividualID = Individual_Incident::_fkIndividualID
You can place a portal to Individual_Incident on the Indivdiuals tab on the Incidents layout to list and select an Individuals record for each given Incidents record. Fields from Individuals can be included in the Portal to show additional info about each selected Individuals record and the _fkIndividualID field can be set up with a value list for selecting Individuals records by their ID field.
For an explanation of the notation that I am using, see the first post of: Common Forum Relationship and Field Notations Explained