Changing from one visa category to another while in the UK is known as 'switching'. There are complicated rules around who is permitted to move from one category to another.
Tier 2 (General)
If a person is on a Tier 2 (General) visa and wishes to change employers, they must obtain a new Certificate of Sponsorship from their new employer and apply for a new visa. The new employer must go through the same steps for employing any overseas (migrant) worker.
All Visitor visas
If a person is here on a visitor visa, they cannot switch to any other category while in the UK. The person must return to their country of origin and apply for a new visa from there.
If a person is on another type of visa, as an employer you should check the relevant Home Office policy guidance document for the visa they wish to switch to, to confirm it is possible from their current category.
It is possible for an overseas (migrant) worker to apply to extend their visa up to the maximum time allowed under their visa category.
For Tier 2 (General) the maximum time is 6 years. However, Tier 2 (General) visas can lead to Indefinite Leave to Remain. For some routes, such as Tier 5 and Tier 2 (Intra-Company Transfer), an extension cannot be granted beyond a certain limit.
The requirements for an extension are similar to those for initial entry.