Use org.apache.commons.lang3.StringUtils conviniene methods for string parsing. Also change Calendar to java.time.LocalDate. Here is a working example:
Rule.java
import java.time.LocalDate;
import java.util.StringJoiner;
public class Rule {
  private String role;
  private LocalDate dateFrom;
  private LocalDate dateTo;
  public Rule(final String role, final LocalDate dateFrom, final LocalDate dateTo) {
    this.role = role;
    this.dateFrom = dateFrom;
    this.dateTo = dateTo;
  }
  @Override
  public String toString() {
    return new StringJoiner(", ", Rule.class.getSimpleName() + "[", "]")
        .add("role='" + role + "'")
        .add("dateFrom=" + dateFrom)
        .add("dateTo=" + dateTo)
        .toString();
  }
}
Main.java
import org.apache.commons.lang3.StringUtils;
import java.time.LocalDate;
import java.time.format.DateTimeFormatter;
public class Main {
  public static void main(String[] args) {
    String mine = "Role = Student; DateFrom = 21/12/2020; DateTo = 10/01/2021;";
    String role = StringUtils.substringBetween(mine, "Role =", ";").trim();
    String dateFrom = StringUtils.substringBetween(mine, "DateFrom =", ";").trim();
    String dateTo = StringUtils.substringBetween(mine, "DateTo =", ";").trim();
    DateTimeFormatter formatter = DateTimeFormatter.ofPattern("dd/MM/uuuu");
    LocalDate localDateFrom = LocalDate.parse(dateFrom, formatter);
    LocalDate localDateTo = LocalDate.parse(dateTo, formatter);
    Rule rule = new Rule(role, localDateFrom, localDateFrom);
    System.out.println(rule);
  }
}
Output (You can format the date as per your preference)
Rule[role='Student', dateFrom=2020-12-21, dateTo=2020-12-21]