You will need to perform a string of upgrades, as there are only so many jumps in version you can make in one step. Have a look through https://confluence.atlassian.com/adminjiraserver073/upgrading-jira-applications-861253088.html
I would recommend:
3.12 -> 3.13 -> 4.0 -> 4.4 -> 5.2 -> 6.4 -> 7.0 -> 7.3
But, you might be able to skip the 3.12 -> 3.13 and possibly 6.4 -> 7.0 steps if your data is not to complex.
Thanks for the information. That is definitely quite a series of upgrades.
Not sure if you can answer these questions but I would also like to know:
1. Which versions of JIRA are currently supported?
2. What cost is involved in performing all these upgrades? We are currently on a JIRA Enterprise: Commercial Server license
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