Akali silent is at a battlefield. Enemy Zenith Blade, moving a unit to the battlefield. Will it also stun Akali now she is in combat when the enemy unit moves?

No — Zenith Blade can't stun Akali here, and the enemy can't even legally choose her as its target.

Akali's passive makes her unchoosable by enemy spells and abilities unless she is in combat, and she isn't in combat at the moment Zenith Blade is played and its target is chosen — sitting alone at a battlefield (even in a Non-Combat Showdown) gives her no Attacker/Defender designation (Rules 758, 355.9.b; her card text). A future state your own spell creates can't retroactively validate the choice (Rule 355.9, cf. FAQ #1492).

It also wouldn't help during resolution: Zenith Blade's instructions run in order — stun first, then the move — and combat designations only get assigned during a Cleanup with an empty chain, well after the spell has fully resolved (Rules 323.2, 459–460). So Akali is still not "in combat" at the instant the stun instruction would apply.

If she were already a participant in an ongoing Combat Showdown (attacker or defender designation) when Zenith Blade is played, she'd be a perfectly legal stun target — but the move alone can't put her in combat in time.