First Solution:
You can call start activity inside your adapter like this:
public class YourAdapter extends Adapter {
     private Context context;
     public YourAdapter(Context context) {
          this.context = context;     
     }
     public View getView(...){
         View v;
         v.setOnClickListener(new OnClickListener() {
             void onClick() {
                 context.startActivity(...);
             }
         });
     }
}
Second Solution:
You can call onClickListener of your button out of the YourAdapter class. Follow these steps:
Craete an interface like this:
public YourInterface{
         public void  yourMethod(args...);
}
Then inside your adapter:
    public YourAdapter extends BaseAdapter{
               private YourInterface listener;
           public YourAdapter (Context context, YourInterface listener){
                    this.listener = listener;
                    this.context = context;
           }
           public View getView(...){
                View v;
         v.setOnClickListener(new OnClickListener() {
             void onClick() {
                 listener.yourMethod(args);
             }
         });
}
And where you initiate yourAdapter will be like this:
YourAdapter adapter = new YourAdapter(getContext(), (args) -> {
            startActivity(...);
        });
This link can be useful for you.