If Ian's injured I could see him spending a year or two on new Avalon being treated and then working up to full health (quite important since he'd want to be back in a 'Mech). It's plausible that he might, given this brush with mortality, decide that the time has come to marry and provide House Davion with a new generation. There's really no information to judge Ian's taste in women, so he could marry for love or he could simply make a political marriage. For the sake of argument, assume that he does the latter, wanting a wife he can leave on New Avalon to look after his children.
At the same time, Hanse probably rises to more prominence since he'd remain the logical choice to take over the Halstead Station raid. (And the Davion brothers were both already superstars of the military). Being Prince's Champion doesn't exclude Hanse from being the heir (if he was Regent for a minor heir, he would be excluded). He's already got some government experience as a military governor (New Aragon) and did well. He and Ian were both quite invested in the project that eventually became NAIS, so that would probably happen.
So by 3015 the picture could be: Ian's married and possibly a father, but raring to go back to the frontlines of the 3SW - almost certainly on the Draconis March. Hanse is acting as his Champion, leading the AFFS as a whole from New Avalon and also with his thumb on various civil roles - he might be titular head of NAIS for example, lending it that prestige - and connections. However, there are several other power players - Aaron Sandoval and Michael Hasek-Davion as Ministers of the Draconis and Capellan Marches, for example. And Ian's wife might be a political hub in her own right, whoever she is.
At some point in the next... five years, say (before Katrina's Peace Proposal)... Ian dies in battle. That raises questions. Should the throne pass to his eldest child, with a Regency? If so, who are the Regents (or sole Regent)? Or, and there's plenty of historical precedent in the Federated Suns, does it make sense to pass the throne directly to an adult heir? In which case Hanse has much to commend himself. Legally, the former is required, but functionally there's a lot of evidence that those laws are relatively easily set aside (Ian succeeded without a regency, Katherine's reign as Archon-Princess...) in favour of practicality.
Hanse might well want to be First Prince, and not just due to ambition - after all, if there's a Regency then Michael Hasek-Davion is a very strong choice since if Hanse is Regent then he's excluded from succession and there's not an overwhelming number of alternatives if Ian's children don't thrive. This could lead to an uncomfortable compromise: Michael as regent but Hanse hangs on as Prince's Champion and Ian's widow acts as a third pole of power - possibly Michael's co-regent.
That could be a very interesting power-struggle, one reflected in internal politics but also external diplomacy and military strategy.