We have a column with client names as a drop down. Our users use this field to select the name of a client whom they are working for. In case the client name does not exist in the drop down, is it possible that the user is able to type inside the field directly and submit the form? 

If that is not possible, lets say we have 'Other Client' as one of the values in the drop down. Once that is selected, is there a possibility to open a new text field where the user will be able to add a new client name and submit?

This is how it is currently implemented in InfoPath. However looking for something similar in Nintex New Responsive Form