Yes. You will need to make a new Tier 4 application in order to join a new course or new sponsor, but you may be able to use an existing Tier 4 visa to enter the UK in order to make that new Tier 4 application.
Your Tier 4 visa is valid for studying a specific course at the instution whose sponsor license number is printed on your visa vignette and biometric residence permit (BRP). You can use this visa to re-enter the UK at any time before the formal end date of the course, to continue your sponsored studies.
If you have now finished the course, but the visa itself is still valid, and you wish to travel to the UK to make a new Tier 4 application for a new course, you can usually use your existing visa to enter the UK. This is confirmed in paragraphs 273-275 of the Tier 4 Policy Guidance. However we advise that you make three checks before travelling to the UK on what the UK Home Office calls "extant leave".
First, check that you are eligible to apply for your new Tier 4 visa from within the UK anyway (see Making a Tier 4 (General) application in UK for more information). If not, you will need to apply from your home country and you can use the Home Office's visa processing times tool to check current processing times in your home country.
Second, check that you meet all these requirements:
- the institution you are returning to study at has a Tier 4 sponsor licence, and they have agreed to sponsor you (or continue to sponsor you) under Tier 4; and
- you have not been reported to the Home Office as having finished your most recent course early, interrupted your studies, or having not enrolled. If the institution that sponsored your current Tier 4 visa has reported one of these matters, it is likely that your visa might already have been 'curtailed' and is no longer valid; and
- you are eligible and can meet the requirements to make a further Tier 4 application from within the UK
Third, carry in your hand luggage evidence to show the Border Force Officer that you will be making a new Tier 4 application before your current Tier 4 leave expires. At the mimmum, this would be evidence that you have already been issued a CAS from your new sponsor institution, and that they have Tier 4 Sponsor status on the Home Office's Register of Tier 4 Sponsors. If you have other evidence, for example some of the documents you will be providing as part of your upcoming Tier 4 application, keep them in your hand luggage for possible checking. The Border Force Officer cannot extend your Tier 4 visa on arrival, but they can allow you to enter the UK in order to make the application.