In order to unlock either of these you will need to have the standard variation of the specific mod. See Velocity: Terminal Addiction for more info on how to unlock them.
Drift tires pro requires you to complete 80, 1000 yard + drifts with Drift tires equipped while on speedlists. Jump nitrous pro requires you to smash 50 billboards (don't have to be unique) while having jump nitrous pro equipped while on speedlists. I recommend jump nitrous pro as it's much easier and faster to get done. This can be done in public lobbies, or you can create a private lobby if you have a friend to help you out. If you activate any speedlists and neither of you drives to meetup, you can keep on working on the pro mods as long as you wish. Whichever you decide to unlock I recommend the new airport for these. There is plenty of wide space for drifts and multiple easy-to-reach billboards.