In the following example from the rulebook, Tyrell attacks Blackwater using two knights from the Reach with support from a knight in King's Landing, resulting in an initial combat strength of 7. If Tyrell instead attacked with one knight from the Reach and moved the other to King's Landing, does the second knight contribute to the support order there (is the combat strength still 7)?
The key idea here is that you first resolve your march order. Then, if you march one or more of yours units "into an area containing units from another House, combat ensues" (rules, page 17).
So, you must first move all your units to the areas that you want. Then if you did move into an area that contains units from another House, you resolve combat. This means that units moved into King's Landing would be able to support the combat as if they were there in the first place.