The phrase "degree discipline" refers to the specific subject or field of study that a person is specializing in while pursuing their degree. Full definition
Equally, if you're applying to a recruitment agency that specialises in a particular field, such as IT, they might prefer, or require, a related degree discipline. (targetjobs.co.uk)
Most engineering degrees focus on one particular discipline (though there are some that let you try a bit of everything) and graduate recruiters typically specify which engineering degree disciplines they accept. (targetcareers.co.uk)
A postgraduate diploma in hotel management is useful for graduates from degree disciplines unrelated to the sector, although many employers will accept HND holders or graduates of any discipline on to their management training schemes. (targetjobs.co.uk)