Can you use close combat expert while making a transporter attack?

no

Filler

To extrapolate on Maraud's correct answer, each of those two abilities requires its own action. You can only assign one non-free action per character per turn

CCE requires a power action and the transporter move & attack ability requires a move action

That applies to powers that require the same kind of action, such as CCE and hypersonic speed. Each requires a power action but a power action can only be used to activate a single ability