Bioware have not released any info that the upcoming Galactic Starfighter xpac is tied in any to the current space reputation.
To gain space reputations, you want to do the hardmode space missions, which you will need level 7 upgrades unless you are really good. So you will need to buy them on GTN from other people/crafters or spend some cartel coins.
There is 1 hardmode space mission available per day, giving out a blue rep every day. The exception is the Sunday one which ask you to do 2 of them and give you a purple and blue.
Here is a guide: http://dulfy.net/2012/12/13/swtor-pa...issions-guide/