DOES NHS SPONSOR BAND 3?

Yes and it should be full time(permanent) with weekly working hours of 37.5 and salary of 25,000+ pounds[ This qualifies for visa sponsorship].  However, not all NHS Trusts are willing to sponsor due to budget constraint. If in doubt, contact the recruitment team(their contact/emails are always on the job advert) to confirm of any available sponsorship before submitting your application if you require CoS before you can take up such position.