As the Cisco 3620 is a modular router, you have to insert cards that suit your needs. As you have a 2514 what use DB60 serial ports you would need to buy a WIC-1T card.
If your 3620 is a bare chassis, you will need a Network Module to insert your WIC-1T card into e.g. NM-1E2W.
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Hope this helps & good luck!