For postpaid subscribers, you can call the hotline and request for a temporary disconnection. Once done, best thing to do is go to your nearest Globe store and present a proof of identification so you can request for SIM card replacement. The old SIM card will be automatically disabled when the new one is activated. Ask for reactivation.
For prepaid subscriber, I believe you need to file for an affidavit of loss at your barangay hall, then go to your nearest Globe store, present your affidavit and proof of identification, and request for SIM card replacement.