In order keep configuration simple, please perform the following steps in Salesforce Classic (Booker25 is Lightning-Ready, you may afterwards use the app in Salesforce Lightning as you please)
A common issue with managed packages is that it's normally not possible to control the order of execution of your own custom triggers in combination with triggers from the managed package on the same record. Booker25 offers a solution to this using pre- and post execution hooks, which allow you to reliably execute your own logic either before or after the packaged triggers fire. At the time of this writing, only the trigger on the Booker25 Reservation object is enabled for hooks. Feel free to contact us if you would like us to enable it for other triggers as well.
Step-by-step guide
Write an Apex class that is global and implements the B25.Util_PluginManager.TriggerHook interface.
Add the preExecutionLogic() and postExecutionLogic() methods with your own custom logic. You can access all the Trigger variables (like Trigger.new) in these methods.
Create a B25__Custom_Setting__c named Reservation Trigger Hook Class. In the field String Value, enter the name of your Apex class.