One of my players wants to improve a primary characteristic from 3 to 4 after having already gone trough 8 career advances. How is this handled? Are 2 of the needed advances considered 'in-career' and the other 2 'out of career'? How many advances does he have to spend in the end?

The player has to transition to a new career and use the advances in that career.

The player can't split the cost of stat improvements between types of advances because the type is dicated by the nature of stat being increased. See the FAQ page 3. Primary stat increases must come from the (up to 6) open advances and non-primary ones from the non-career advance lines (up to 4). The fact there are only 6 and 4 is part of the limits on the ability to improve such stats (if you could use non-career advances you would break this).

Rob

From what the errata I would say it would be an out of career advance. The errata clafies that any "in career" advance used after career progress advances have been used up count as "out of career" advances. While they still have remaining career progress slots they don't have enough so I would say the same rule applies. This means it would cost 5, take up one of the two "out of career" progression slots but leaves the remaining 2 in-career slots for other uses.