I don't know based on the rulebook. The rulebook context defines the Zealous attribute as: "This Unit is deployed active (not exhausted) on the battlefield" (page 21). However, it does not specify what happens if a Unit already on the battlefield is granted Zealous by an effect, nor does it clarify whether the attribute has any effect outside of deployment.

To answer this question definitively, the rulebook would need to specify:

• Whether gaining Zealous after deployment causes a Unit to become active immediately, or
• If Zealous only affects the state of a Unit at the moment it is deployed.

Without this information, the rulebook is insufficient to provide a clear answer.

Source: Core Rulebook (pp. 14, 15, 19, 21, 24)