Failing a Module in Masters

I have failed a module in my masters in the UK in the 1st semester. I am in the University of Sussex. I haven't gotten the results but based on the paper, I can guarantee that I will fail. Any idea about how and when does re-sit exams take place? I want to try for a full time job from September and that will be only possible if I have a degree in hand.

Based upon your "I can guarantee that I will fail" comment, I'm assuming that we're not talking about a marginal fail (45 - 49%), in which case automated compensation may have applied. (See paragraphs 71 through 73 of Postgraduate [Progression and] Award Regulations 2024-25.)
The timing of reassessment is supposed to be detailed in Conduct for Examinations and Changes to Examination and Assessment Arrangements, but that just refers you to Timetable for exams, which refers you to Resitting an assessment, which says, "Go to Sussex Direct for information about what kind of resit you’re doing and when it takes place."
However, if you look at Term dates you will note that it says, "Resit assessment period (all modules)" is "Mon 4 Aug to Sat 16 Aug 2025". (Different dates apply to distance learning modules).

I want to try for a full time job from September and that will be only possible if I have a degree in hand.

I would check with your school/department as to when you will be given your final result (even if you do pass the module you're worried about).
At another university I'm familiar with (i.e. not Sussex) the dissertation submission deadline for taught postgrads is the end of August. At that university there is no way a taught postgrad will have their degree result in September -- and their graduation ceremony would be in the January/February period. Obviously Sussex's dates might be different -- so you need to check that.