I am a school teacher
As a qualified school teacher you are already fully qualified to work in the FE & Skills sector. There is nothing to stop you applying for jobs as you find them. Although the job adverts may refer to other teaching qualifications [eg DET], your PGCE/QTS is fully recognised in the sector. Many teachers come into FE & Skills from schools wishing to teach literacy, numeracy, ESOL and/or Special Educational Needs [SEN]. If so you may wish to consider the subject specialist diplomas which relate to these fields [for details see here]. These may be referred to in job adverts or at interview and a willingness to undertake these may be expected.
The FE & Skills sector is extremely wide and new entrants may wish to familiarise themselves with the scope and nature of the component parts. A document entitled orientation guidance was produced a few years back for exactly this purpose and whilst is may now be a little dated, it might provide a useful starting point if you are starting from scratch. You can request a copy from us: email firstname.lastname@example.org or call us 0300 303 1877.