The Apprenticeship Levy is a 0.5% charge on an employer's pay bill, introduced in April 2017 to fund apprenticeship training. For most contractors it is relevant not as a charge on their own PSC (which is far below the £3m pay-bill allowance) but as one of the employment costs that comes out of an umbrella assignment rate.
When a contractor works through an umbrella company, the umbrella is the employer and its pay bill is large enough that the levy applies. The levy is therefore funded from the assignment rate, alongside employer National Insurance at 15% and the umbrella's margin, before the contractor's gross salary is arrived at. A compliant umbrella will show it as a separate line in the Key Information Document.
The levy is also charged on the fee-payer for an inside-IR35 engagement under Chapter 10, on top of employer NIC, when calculating the deemed direct payment. So whether a contractor is inside IR35 through their PSC or working through an umbrella, the Apprenticeship Levy is one of the costs that reduces the effective rate compared with an outside-IR35 PSC engagement.