Hi if you are applying to an organisation which is not a Sponsored Licence Holder then you will, sadly, come up against this as a problem, as many organisations will not wish to go through the time and cost for perhaps one or a handful of jobs.
You do not need to be sponsored to be on a Graduate Visa so depending on how long you have left on that visa, you can simply declare that you currently have the right to work in the UK. But given you will ultimately not have many other options but to apply for a Skilled Worker Visa, your options may be restricted, sadly - and depending on your skill and salary level, there may not be an Occupation Code that is sponsorable.
You could target your efforts towards organisations that are already Sponsors (there is a list on the Govt website). You could keep silent about your status unless asked but if you are offered the job and for whatever reason the company is unable to sponsor you or you cannot otherwise demonstrate a right to work in the UK then the offer would have to be withdrawn.
We are a sponsoring organisation but there are times when we state clearly in the advert that it's not a job we can sponsor so that applicants are clear from the outset.

Many thanks for your thoughts Helen. I think the mistake we make most times as prospective employees is the fact that we let employers know we want to work for them because of sponsorship. I have come to realise this is a red flag for most employers. I have heard of employers in the UK going above and beyond to get a sponsorship licence because of an outstanding employee who needs sponsorship. Saad,I would advice you continue to gather some valuable UK HR experience with your present visa and stop talking about sponsorship at the interview stage. Wishing you the very best.

In reply to Oluwamuyiwa Ayeni:

I do think it's really difficult for employers who are not already sponsors, but of course I totally appreciate how demoralising it is for the job-seeker! Obtaining and maintaining sponsorship licences are costly and time consuming and many organisations may take the view that for one candidate, however outstanding, it's not worth it. Others may think it worth obtaining a licence for one candidate in case that opens up their talent market (but it will depend on whether they have many roles that are sponsorable). But it's also a sad fact that even those of us with sponsorship licences are at the mercy of the Home Office and Government constantly changing the rules, skill levels, salary thresholds etc and therefore we can't rely on having a sponsorship licence even to employ some of the "brightest and best" if there is no other way for them to legally work in the UK.

In reply to Helen:

Helen, Your points are valid! The salary threshold is a major factor the Home Office could look into again in ensuring that smaller companies in the UK can afford to sponsor some of the 'brightest and best' talent around. This could even be a major benefit for the Home Office and the UK government as illegal immigration could also be reduced to the barest minimum.

Unfortunately the role you apply to needs to be on the Shortage Occupation list, so it's not so much about the applicant as the role. HR roles don't appear on this list.

In reply to Annabel:

Well, I believe there are HR roles are on the Shortage Occupation list with Occupation Code-3562 which consists of 'Human Resources and Industrial Relations Officers'. Unless the rules have just recently been updated. www.gov.uk/.../skilled-worker-visa-eligible-occupations-and-codes

In reply to Oluwamuyiwa Ayeni:

Apologies, I stand corrected! I hadn't thought that was the case...

In reply to Annabel:

Hi, there is a Standard Occupation Code for HR professionals as Oluwamuyiwa states, code 3562 which means if the salary and skill level are met (currently £25,600) then someone can be sponsored in that role if they can achieve 70 points under the Points Based System through job offer, qualifications, salary level, English Language requirements etc.

There is, separately, a Shortage Occupation List which means that tradeable points can be used if the salary is below the threshold. HR is not on the Shortage Occupation List but individuals can still be sponsored if they meet the criteria referred to above.

However, the Govt has indeed looked at salary thresholds but sadly, for the most part, they are all INCREASING!

The Skilled Worker ‘going rate’ salary thresholds are all increasing and the general/ minimum thresholds are increasing from £25,600 to £26,200 and from £20,480 to £20,960. Many of the Skilled Worker "going rates" are higher than the general threshold and it is always the higher of the two rates that needs to be paid.

The calculations are all also changing from being based on a 39 hour week to a 37.5 hour week which means that the actual hourly rate will increase in some roles quite significantly:
www.gov.uk/.../statement-of-changes-to-the-immigration-rules-hc-1160-9-march-2023

The actual Guidance for Employers will probably only be updated around 11 April (if we are lucky!).

No good news.......

In reply to Annabel:

No worries at all. Helen has just helped to shed more light on this. I just learnt something new too.

In reply to Helen:

Definitely no good news!!! Absolute so difficult for employers to meet these salary thresholds.