Extracurricular activities can serve two purposes when considering applications to selective schools. First, engaging in extracurricular activities can demonstrate that the applicant is well-rounded. While selective schools emphasise past academic achievement (as an applicant) and favourable performance (as a student), they also encourage students to expand their strengths beyond academic capabilities, which can be done through extracurricular activities.
Second, extracurricular activities can help selective schools differentiate between individual applicants, allowing them to make more informed admission decisions. For example, if Applicant A and Applicant B have received similar grades at their current school and if they have performed at a similar standard in the HAST, the school can compare each applicant's involvement in extracurricular activities, which can assist in determining the student who will be more suitable considering aspects such as the school's values. However, it must be stressed that high grades alongside favourable performance in the HAST remain essential in maximising your chances of receiving an offer.
In terms of getting involved in extracurricular activities, there are a range of activities that you could participate in. Depending on your interests, you could play sports, volunteer, join certain clubs/communities, and so on. Applicants to selective schools seem to engage in a combination of these.
I hope this helps!