The Lions Club supports an Eye Bank in Washington and Idaho; the Eye Bank performs over 400 cornea transplants each year. Frequently donated corneas from deceased persons must be specially packed and delivered by bus or train to the donor's location, requiring a volunteer to pick up the package and deliver it to the hospital.
I have two questions
1. I would like to know the subject of "require".
2. I wonder if "requiring" is gerund or anything.
The process of transporting and delivering packages is the subject of require. Requiring functions as a transitive verb in your example. To better perceive its function, you can simply re-write it as: "This (the statement before 'requiring') [requires] that." If you want to make it gerund, you could re-write it as: "Requiring additional materials makes the task of applying to college arduous."