My opponent has Terrax and SWAT Specialist. They are adjacent.

At the beginning of the turn can the SWAT specialist utilize his TA to up Terrax's damage and then have Terrax use his running shot carrying the SWAT? (so that the SWAT guy can be sat down adjacent to terrax to use the SHIELD TA?)

Thanks in advance for any answers!

SHIELD does not activate until the ranged combat attack is being declared. This means that the SHIELD adjacent must be adjacent at the start of the ranged attack, and he must be given his power action at the start of the ranged attack. In the instance above, you're attempting to use the SHIELD ability before there is a ranged attack to boost, and so it can't be done.

You can't use SHIELD before Terrax has moved, and you can't use SHIELD after being carried. For this reason, you can't use SHIELD in your scenario unless Terrax's Running Shot brings him naturally into another square adjacent to the SHIELD agent.

So you can perform an action during the middle of an action? In your last few sentences that is what it sounded like. If Terrax performs running shot that power action isn't resolved until the dice have been rolled, right? So if you use running shot and move terrax up to where the SWAT specialist and then "chip" the swat specialist for use of his team ability you would be performing an action during the middle of Terrax's action...or am I way off base?

Typically, you can not perform another action until the previous one is resolved. However, SHIELD by its very nature has to occur mid-action (whenever the character makes a ranged combat attack). So in this case, the SHIELD member is being given an action during the RS action but it's an exception to the general rule.