After the application form and a psychometric test/video interview, what usually comes next when applying for a vacation scheme is the assessment centre phase. Law firms are usually choose which types of exercises are included within the assessment centre, but tasks such as group and written exercises are some of the most common ones.
One of my favourite websites, Lawcareers.net, published an outline of what to expect during an assessment centre and what skills you need to polish in order to succeed.
Training contract assessment centres: everything you need to know - Features (lawcareers.net)